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Math Tutorials
United States
Приєднався 27 бер 2020
Mathematics videos designed to present college algebra, trigonometry, precalculus, and calculus topics.
Section numbers correspond to:
Algebra and Trigonometry, 1st ed, by Abramson, Belloit, Falduto, Gross, Lippman et al.
It is an open-source textbook from OpenStax. Download for free at link below. Text is licensed under the Creative Commons Attribution license. creativecommons.org/licenses/by/4.0/
Business Calculus, 1st ed, by Calaway, Hoffman, Lippman
This textbook was created by Shana Calaway for the Open Course Library, remixed from Dale Hoffman's Contemporary Calculus text. It was extended by David Lippman to add several additional topics. The text is licensed under the Creative Commons Attribution license creativecommons.org/licenses/by/3.0/us/. Download link below.
Many of these videos have also been embedded in the My Open Math online homework system.
Section numbers correspond to:
Algebra and Trigonometry, 1st ed, by Abramson, Belloit, Falduto, Gross, Lippman et al.
It is an open-source textbook from OpenStax. Download for free at link below. Text is licensed under the Creative Commons Attribution license. creativecommons.org/licenses/by/4.0/
Business Calculus, 1st ed, by Calaway, Hoffman, Lippman
This textbook was created by Shana Calaway for the Open Course Library, remixed from Dale Hoffman's Contemporary Calculus text. It was extended by David Lippman to add several additional topics. The text is licensed under the Creative Commons Attribution license creativecommons.org/licenses/by/3.0/us/. Download link below.
Many of these videos have also been embedded in the My Open Math online homework system.
Sum and Difference Formulas for Sine in Radian Measure
In this math example, we are trying to use a sum or difference trig formula to calculate the exact value for angle in radian measure. We want to use the most common radian angles pi/6, pi/4, and pi/3 to do this calculation because these are known ratios. Each of these examples have given radian angles that have denominators of 12. Because of this, we first rewrite pi/6 as 2pi/12, pi/4 as 3pi/12, and pi/3 as 4pi/12. This makes the process of identifying which angles add or subtract to make the given angle easier.
sin(5pi/12)
The first example can be completed by using two angles that add together. We use the sum formula for sine to fill into the formula. I try to show where each angle is substituted into the formula by using color coding. After the problem is rewritten using our common angles, we fill in with the appropriate ratios to evaluate each trig function (sine and cosine). The answer is then simplified completely.
sin(13pi/12)
For the second problem, we are given an angle larger than pi. Because of this larger angle, no two pairs of our common angles add together to our given angle. Therefore, we want to find a reference angle. This means placing the given angle into the correct quadrant, drawing in our reference angle (always to the x-axis), and calculating the reference angle by subtracting the smaller angle from the larger that make up the reference angle. When we replace the original angle with the reference angle, we also must check to see the overall sign (positive/negative) of the function. I like to use the phrase "All Students Take Calculus" to remember in which quadrant each function is positive. This leads us to include a negative in front of our function that carries along when we fill into the difference formula for sine. The angles that are filled in for each piece of our formula are color coded to help see where they were filled in. After using the difference formula, we evaluate each of the known trig functions to give us nice exact ratios. The solution is then reduced fully to give the best solution possible.
This video contains examples that are from Algebra and Trigonometry, 1st ed, by Abramson, Belloit, Falduto, Gross, Lippman et al. It is an open-source textbook from OpenStax that you may download for
free at openstax.org/details/books/algebra-and-trigonometry. The text is licensed under the Creative Commons Attribution license. creativecommons.org/licenses/by/4.0/
sin(5pi/12)
The first example can be completed by using two angles that add together. We use the sum formula for sine to fill into the formula. I try to show where each angle is substituted into the formula by using color coding. After the problem is rewritten using our common angles, we fill in with the appropriate ratios to evaluate each trig function (sine and cosine). The answer is then simplified completely.
sin(13pi/12)
For the second problem, we are given an angle larger than pi. Because of this larger angle, no two pairs of our common angles add together to our given angle. Therefore, we want to find a reference angle. This means placing the given angle into the correct quadrant, drawing in our reference angle (always to the x-axis), and calculating the reference angle by subtracting the smaller angle from the larger that make up the reference angle. When we replace the original angle with the reference angle, we also must check to see the overall sign (positive/negative) of the function. I like to use the phrase "All Students Take Calculus" to remember in which quadrant each function is positive. This leads us to include a negative in front of our function that carries along when we fill into the difference formula for sine. The angles that are filled in for each piece of our formula are color coded to help see where they were filled in. After using the difference formula, we evaluate each of the known trig functions to give us nice exact ratios. The solution is then reduced fully to give the best solution possible.
This video contains examples that are from Algebra and Trigonometry, 1st ed, by Abramson, Belloit, Falduto, Gross, Lippman et al. It is an open-source textbook from OpenStax that you may download for
free at openstax.org/details/books/algebra-and-trigonometry. The text is licensed under the Creative Commons Attribution license. creativecommons.org/licenses/by/4.0/
Переглядів: 18
Відео
Finding area of triangular lot by using frontage measurements
Переглядів 903 місяці тому
In this math example, we are trying to find the area of a triangle but it is not as simple as filling into the triangle area formula 1/2(base)(height) because we are not given the height. Instead, we must use Heron's formula. To do so, we first find the semi-perimeter by adding together all three side lengths and dividing the result by 2. We then show all the work to use our semi-perimeter and ...
Solve a trig equation by using a double-angle formula
Переглядів 383 місяці тому
In this math example, we find all solutions to a trigonometric equation on the interval from 0 to 2pi. This problem begins with both cosine of a single angle and cosine of a double-angle as part of the equation. Our first step is to replace the cos(2theta) with 2cos^(theta)-1 by using the double-angle identity. Next, we work to get all of our terms on one side of the equation and zero on the ot...
Solving a Trig Equation using Pythagorean Identity
Переглядів 643 місяці тому
In this math example, we find all solutions to a trigonometric equation on the interval from 0 to 2pi. This problem begins with both sine and cosine as part of the equation. Our first step is to replace sin^2(theta) with 1-cos^2(theta) by using the Pythagorean identity. Next, we work to get all of our terms on one side of the equation and zero on the other. We go ahead a rewrite our equation so...
Difference formula using Reference angle (Easy Way)
Переглядів 434 місяці тому
In this math example, we are trying to use a sum or difference trig formula to calculate the exact value for a larger degree angle. We want to use 30, 45, or 60 degrees to do this calculation because these are known ratios. Because of this larger angle that we are given, no two pairs of those angles add together to our given angle. Therefore, we want to find a reference angle. This means placin...
the easiest way to use sum and difference trig formulas for big angles
Переглядів 754 місяці тому
In this math example, we are trying to use a sum or difference trig formula to calculate the exact value for a larger degree angle. We want to use 30, 45, or 60 degrees to do this calculation because these are known ratios. Because of this larger angle that we are given, no two pairs of those angles add together to our given angle. Therefore, we want to find a reference angle. This means placin...
Use the difference formula to simplify tangent
Переглядів 274 місяці тому
In this math example, we want to use the difference formula for trig functions to simplify an expression as much as possible. Initially, we attempt to use the difference formula for tangent but after filling in, we realize that evaluating will be difficult because tangent is undefined at the values we are trying to use. To get around this, we use a quotient identity to first rewrite out tangent...
Use the difference formula for cosecant
Переглядів 314 місяці тому
In this math example, we first use a reciprocal identity to rewrite the cosecant function as 1/sine. (csc = 1/sin) The difference formula for sine is then used to simplify a trig expression. To do so, we first identify what values will be filled in for each part of the formula (alpha and beta). They are filled in and we simplify by evaluating sine and cosine at the given angle. csc(pi/2-u) This...
Use the difference formula for sine
Переглядів 234 місяці тому
In this math example, we use a difference formula for sine to simplify a trig expression. To do so, we first identify what values will be filled in for each part of the formula (alpha and beta). They are filled in and we simplify by evaluating sine and cosine at the given angle. sin(u-pi/2) This video contains examples that are from Algebra and Trigonometry, 1st ed, by Abramson, Belloit, Faldut...
use the difference formula for cosine
Переглядів 184 місяці тому
In this math example, we use a difference formula for cosine to simplify a trig expression. To do so, we first identify what values will be filled in for each part of the formula (alpha and beta). They are filled in and we simplify by evaluating sine and cosine at the given angle. cos(pi-t) This video contains examples that are from Algebra and Trigonometry, 1st ed, by Abramson, Belloit, Faldut...
solve trig equation by factoring out a common factor
Переглядів 594 місяці тому
In this math example, we solve a trigonometric equation of the quadratic type that involves cosine (cosx). We approach this problem by having all of the terms on one side and zero on the other. With this, we think about how to factor. In this case, we are able to factor out a common factor or cosine from each term. Each factor is then set equal to zero and solved for cosine. Cosine now equals s...
Factor and solve trig equation with sin(theta)
Переглядів 764 місяці тому
In this math example, we solve a trigonometric equation of the quadratic type that involves sine (sinx). We approach this problem by first using a "Let" statement to replace each sine with x. This makes our equation look like a quadratic equation that most are more comfortable with solving. We choose to use factoring by the AC method. Each factor is then set equal to zero and solved for x. Then...
Use calculator to help solve trig equation
Переглядів 364 місяці тому
In this math example, we solve a trigonometric equation involving cosine (cosx) with the help of our calculator. Because our problem starts with cosine on one side of the equation, we begin by applying arccosine (inverse cosine function cos^-1) to both sides of the equation. This produces a value for our angle. We determine the quadrant that this angle lies in and also find the reference angle ...
Use calculator to solve trig equation involving secant
Переглядів 264 місяці тому
In this math example, we solve a trigonometric equation involving secant (secx) by first rewriting it in terms of cosine (cosx) by using a reciprocal identity. Then we solve the equation to have cosine (cosx) on one side by itself. We then utilize our calculator to find a decimal approximation in radian measure. It is determined that this solution is in the 2nd quadrant. We next find a referenc...
Solve trig equation with tangent (tanx)
Переглядів 544 місяці тому
In this math example, we solve a trigonometric equation involving tangent (tanx). To do so, we treat it as a linear equation and work to isolate the tangent on one side by itself and move the constants to the other side of the equation. This requires some distributing and adding or subtracting of terms to move from one side to the other. After tangent is isolated, we think about the graph of ta...
Find angle between guy-wires using difference formula for tangent
Переглядів 1254 місяці тому
Find angle between guy-wires using difference formula for tangent
tangent thought of as slope using difference formula
Переглядів 524 місяці тому
tangent thought of as slope using difference formula
Rewrite using the cofunction identity
Переглядів 344 місяці тому
Rewrite using the cofunction identity
Use Even/Odd identity to verify trigonometric identity
Переглядів 874 місяці тому
Use Even/Odd identity to verify trigonometric identity
graph complicated secant function by hand
Переглядів 184 місяці тому
graph complicated secant function by hand
Path of point around circle as a cosine function
Переглядів 214 місяці тому
Path of point around circle as a cosine function
Related rate area of triangle for ladder pulled away from wall
Переглядів 1794 місяці тому
Related rate area of triangle for ladder pulled away from wall
How to use calculator to find cosecant csc and cotangent cot
Переглядів 514 місяці тому
How to use calculator to find cosecant csc and cotangent cot
Use reciprocal and quotient identities.
Переглядів 185 місяців тому
Use reciprocal and quotient identities.
Use reference angles to find additional angles for sine and cosine
Переглядів 715 місяців тому
Use reference angles to find additional angles for sine and cosine
This is amazing and soooo underrated! Thank u so much (this video rlly helped)
this video explained it so much better than my trig teacher, bless 🙏
Very helpful 👍
YOU SUCK, where the hell did pi go???? following this tutorial made me waste hours.
Why central angle egual to arc
Thank you this is much better than myopenmath
Thanks man
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Good
Thank you sir
Thank you so much for making short and Understandble yt vids its really helping my calc journey
Your process is so complicated bro
thanks alot!
This was very helpful😀
How do you when what points to plot on the slope
Slay
Thanks so much this was used in my assignment but reverse image search has saved me
Good 👍
thank you so much for this i got a 100 on my final🙏
Super helpful thank you!
Thank you! Much appreciated!
Thank you for all of your helpful content, the effort you put into your videos doesn't go unnoticed and It helps many students such as myself. Thank you for taking the time to make these for us.
Thank you. I really appreciate your kind words.
saving my life thanks man
omg you the MOM person i aint even realize
The only video that helped. Thank youuu! God bless!
why was u-substitution used when this can more simply be integrated directly
blud wants to flex his calc skills
THANK YOU SO MUCH
Thank you!!!! This was very insightful! 😁
I wish you could have simplified it further :(
Thanks for this meticulous guide! Helped me with my homework :D
Thank you❤❤😊 you just saved me hours of headache.😢
Thank you❤❤😊 you just saved me minutes of headache.😢
well definitely did the left and her mom def did the right 😉😉 6:25
What if the graph given doesn’t show it’s y intercept and it doesn’t give us a point where x is = 0?
Thank you so much 😁❤
in plain english to a 10 year old, what is the function describing or minmising it describing? We are saying in this independent variable / cost function relationship, this is the amount of X that will give you the lowest cost possible for this particular relationship? we are optimising this functional relationship to get a local/global min? so using this value of x for our dependant variable should yield the best results possible in the case of what we want to optimise?
Thanks sir .... subscribed
Out of every other videi yours is the best🤌🏻
✅
life saver, thank you
Thankyou❤❤🎉🎉
🏃 Promo'SM
Thanks I love u
Welcome 😊
saved my neck in calculus class! thank you sir!
Very welcome!
Thank you so much! This video deserves more appreciation!
Thanks. Glad it helped.
THANK YOU.
You're welcome!
i watched this 4 times and each time its just as confusing. can you redo this with rules of what needs to go where, because of what? this video is really difficult.
Because you are trying to graph the derivative based on the original function's graph, you need to find slopes of tangent lines to the given graph (think rise/run). The first one that I try to identify is when we have a horizontal tangent line (slope zero). This occurs at x= -1, so we get the point (-1,0) for the derivative's graph. The next point that I find is at x = -3 when the slope of the tangent line is -1 (gives point (-3,-1) for derivative's graph). The process is repeated at x=1 and x=3 to attain points (1,1) and (3,2). With these points on the derivative's graph, we draw a line that connects the points to give us the derivative of the function. Make sure to extend your line over the entire given interval. This video probably could have been clearer if I had included a t-chart for the points on the derivative function as I found them.
Thank you!! Just helped me out big time!
Great. Glad to hear that it helped.
We have the same number of subs lol
Wanna say thank you to you for all your efforts and hardwork 👍👍
I appreciate that!
Thank you for explaining this. It's much easier to understand it now! ♥
You're so welcome!