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...