# identities

1. ### Equating trig identities

Hi, I hope someone can help. It would be great if someone could explain how 2((secx)^4 + 2(secx)^2(tanx)^2) equals -2(cos(2x)-2)(secx)^4 I know that the expressions are related in some way, I just can't pinpoint what. - Olivia
2. ### Finding the second derivative of trig function

Hi, I hope someone can help. I'm trying to find the second derivative for the trigonometric function y = sinxtanx Apparently the first derivative is y' = sinx + secxtanx even though I got y' = cosxtanx + sinx(secx)^2. I must of missed a step and would appreciate help. The second derivative...
3. ### Proving identity

Hi, Does the following expression represent an identity? A student of mine created the expression above and believes that it is an identity. However, I subbed in pi/4 for x on both sides and I got different answers... therefore disproving it as an identity. Can someone please confirm this...
4. ### Inverse reciprocal trig functions

Hi, I hope someone can help. Can someone please explain to me why sec^1(x) does NOT equal 1/cos^1(x) and why sec^1(x) does equal cos^1(1/x)? The notation can get a bit confusing. Thanks, Olivia
5. ### Solving trigonometric linear equation

Hi, I hope someone can help. I would like some clarification on solving trigonometric functions. Let me provide an example: Is there a way to directly solve for 3t on my calculator? From what it seems, you have to first solve as if the equation is cost = 1/2 and then (assuming that the...
6. ### Multiply v.s. dividing trig identities

Hi, Can someone please explain why cos2x / (1/2)Sin2x is equivalent to 2 x (cos2x/Sin2x)? Thanks, Olivia
7. ### Proving an identity

Hi, I hope someone can help. I'm trying to understand the process of proving an identity. Let's say that you were trying to prove the following equation: sin2x/(1+cos2x) = tanx I know that the equation is an identity since when I simplify the left-hand side, it is equivalent to the...
8. ### Verifying equivalent trig ratios

Hi, I hope someone can help. I'm suppose to prove that sin(2pi/3) = sin(8pi/3) based on the formula that I developed: Sin4x = 4SinxCos-8Sin^3Cosx This is the textbook solution for the question: I believe what the solution is trying to say is that we already know sin(2pi/3) since (2pi/3)...
9. ### Developing a double angle formula for Sin4x

Hi, I hope someone can help. I'm just trying to understand how Sin4x can be placed into a double-angle formula. One of the ways that I came across is as follows: Can someone please tell me the thought-process behind the first-step? I know that 2Sinx= 2SinxCosx, but where does the (2) and...
10. ### Double angles and trig ratios

Hi, I hope someone can help. I'm trying to rewrite the trig ratio cos3x to fit within a double angle formula. These are the steps which I have followed: https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.182274.html While I understand the steps...
11. ### Simplifying trigonometric expression

Hi, I hope someone can help me properly simplify the following expression: The solution is apparently Sincerely, Olivia
12. ### Trig identities

Hi, I hope someone can help. I'm suppose to show that the following equation is true given the diagram shown: The textbook solution is as follows: I'm confused how we could possibly get the coordinates (-y, x), as explained above in the solution. It just does not make any sense to me. It...
13. ### Calculating inverse trig function

Hi, I hope someone can help. How does my calculator know what the range restrictions are on a inverse trig function? I know that inverse trig functions have a one-to-many mapping, so you must restrict the range. For example, I know that for arccosin it is convention to restrict the range...
14. ### Some questions to do with trig identities (I think)

I have no idea how to do this stuff so here I am. I need to simplify these three problems: sin^2θ+sec^2θ+tan^2θ+cos^2θ x+sin^2xsecx (cscx+1)(cscx-1)
15. ### complement and supplement identities problem

Hi everyone. I need help on the following problem: (1/sinx)-(1/tanx) = tan(x/2), where x is in degrees. How do you reduce the "left hand side" to the "right hand side" using trigonometric identities? Thank you.
16. ### Sum and difference identities help?

The following relationship is known to be true for two angles A and B: cos(A)cos(B)-sin(A)sin(B)=0.957269 Express A in terms of the angle B. Work in degrees and report numeric values accurate to 2 decimal places. Enter your answer as an expression. Be sure your variables match those in the...
17. ### Trig Identities

I have the following question, i am finding hard. \sin2\theta-1=\cos2\theta minus the \cos2\theta \sin2\theta-1-\cos2\theta=0 Is the next move with the identity to change it to \sin2\theta-1-1-2\sin^2\theta=0 Or am i going in the wrong direction? Any help would be much appreciated...
18. ### Trig. Identities Help?

Create a trigonometric identity that contains at least 3 different trigonometric identities. Explain how you created it and know it is an identity.
19. ### Prove using Product to sum identities

Prove Cos (α – β) = cos α cos β + sin α sin β Hint:Keep the left side as is and use the Product to Sum Identities. Then, distribution to simplify the right side. I could really use some help on this..
20. ### Proving identities

Hey, I used to teach math ~15 years ago. Today a friend asked me to help her kid with some trig. I'm out of my depth! - and don't have the time right now to re-learn trig. There are two "Prove the identities" problems - below. Would great appreciate any help listing the steps involved...