# trigonometric

1. ### Trigonometric Integrals

I'm studying how to do this particular problem and I'm just going to give you a piece of it. Here in this picture/step of the problem 15/4 turned into positive 15/8 instead of negative 15/8 when multiplied by -1/2. What's the deal?
2. ### Trigonometric Integrals

How did they get (sin^(6)x/6)+C as their answer?
3. ### Trigonometric Integrals: Odd power of cosine

The tittle should have said Odd power of sine, not cosine..... Please click on the image for my question. Thanks!
4. ### Limit of trigonometric function?

so i added and subtracted 1 in numerator so numerator looked like this: 1+1-1-sqrt(cosx) = 2-1-sqrt(cosx) but i got infinity - infinity, so this wasn't such a good idea, i multiplied both numerator and denominator by 1+sqrt(cosx) but still nothing, i tried some trigonometric transformations...
5. ### Proof including inverse trigonometric functions.

Prove that: arctan(x+y)<y+ arctanx y>0, x real number. I don't know even how to start, usually with problems like this i use Rolle's or Lagrange's theorem but here, i can't prove it that way.
6. ### Help needed in solving a trigonometric equation

How is the following equation solved? sin^4(7x) + cos^2(8x^4-9x) = 0 I am under the impression that the equation actually has no solutions. But how to verify or prove this?
7. ### Trigonometric Limit

Find the limit of (1 - cosx)/(x^2) as x tends to 0. The answer is 1/2. I know that the limit of (1 - cosx)/x as x tends to 0 is zero. I decided to separate the original expression given this way: 1/(x^2) * (1 - cosx)/1 I then multiplied the top and bottom of the expression (1 - cosx)/1 by...
8. ### Trigonometric Equation

Here is my work: 4cos(2x + 30) + 1 = 1 4 cos(2x + 30) = 1-1 4cos(2x + 30) = 0 Dividing both sides by 4, I got: cos(2x + 30) = 0 Take the inverse of both sides. arccos[cos(2x + 30) = arccos(0) 2x + 30 = 0 2x = -30 x = -30/2 x = -15 Is this correct?
9. ### Trigonometric Limits

Find the limit of (x^2)*sin(1/x) as x tends to 0. I know that the limit of (sinx)/x = 1 as x goes to zero. I am suppose to convert (x^2)*sin(1/x) to (sinx)/x algebraically before proceeding to find the limit. What is the proper procedure in this case?
10. ### sin^4(Ө) = 3/8-3/8 cos(2Ө). Prove the trigonometric identity

So far I have gotten that i need to expand the equation so I separated the equation into (1- cos^2Ө)(1- cos^2Ө) = 1- 2cos^2Ө + (cos^2Ө)^2. I reduced it because sin^2Ө = 1 – cos^2Ө and after that I'm lost. I think I am supposed to use the power reducing formula but i dont know how to get it...
11. ### Trigonometric Identities

Dear all, I have worked out tanAtanB but have trouble finding tan A + tan B (As per my working) Please help. Thanks in advance
12. ### Find All Six Trigonometric Functions

Given the point (0,2) on the terminal side of theta in standard position, find the exact value of the six trigonometric functions of theta. I can do this problem if the given point did not include a zero. How do I solve this problem when either the x or y coordinate is zero? In this...
13. ### Infinite trigonometric series

Hi all, an interesting infinite series question for you: show that $\displaystyle \sum_{r=1}^\infty 2^{1-r} \tan\left(\frac {x}{2^r} \right ) = \frac 2x - 2\cot x.$ It was posed to me by someone else and I don't much care for the actual solution, but any tips would be welcome. Thanks!
14. ### Using substitution to evaluate the integrals involving trigonometric functions

How did they get 1/4? I find it confusing when dealing with trig functions. I've showed my workt, I hope someone catches my error. Thanks!
15. ### Evaluating indefinite integral using substitution involving trigonometric functions

The correct answer highlighted in yellow -csc2(4x)+C. I got something similar to that (2csc2(4x))/-3. What did I do wrong?
16. ### quick question about the antiderivative of this trigonometric function

Please click the image for my question. Thanks.
17. ### Trigonometric Identities

Suppose −π/2< x < 0 and sin(x) = −√5/3, and cot(y) = 2√2. Find theexact value of cos(x) + cos(4y). Using cos^2(x)+sin^2(x)=1, I worked out that cos(x)=2/3 but that doesn't seem to satisfy the condition that − π/2 < x < 0. Please help. I have found cos(y) using cot*y)=1/tan(y) and the sec...
18. ### Trigonometric Identities

Need help understanding the question: If sin t=c, 0 < t < pi/2, find in terms of c: (a) sin(pi-t) (b) cos(-t) Do I need to use this type of function?: sin(a-b) = sin(a)cos(b) - cos(a)sin(b) And how would state my answer that it is 0 < t < pi/2 Thanks
19. ### Trigonometric and hyperbolic identities

Hi Im struggling with this question would be greatful for some advice. Thanks Q1. Involves trigonometric identities and an understanding of polar and Cartesian coordinates. Note that Sin and Cos are cyclical, ie. there is more than one angle for each value, so if the first gives an...
20. ### Derivative of trigonometric functions

How is the answer 0? I provided my work to show my train of thought.... Is there an easy way of solving this?