# Trig Functions .

1. Sep 4, 2006

### arizona_cards_11

Trig Functions.....

I don't really understand how my book wants me to approach this problem. And I know that you appreciate work....because this is for my benefit after all....but how exactly would this be worked?

Direction: Solve the equation for (theta)..... 0 is less than or equal to (theta) < 2*pi

2sin^2(theta) = 1

(theta) = (pi/4) , ((3*pi)/(4)) , ((5*pi)/(4)) , ((7*pi)/(4))

2. Sep 4, 2006

### d_leet

This should be a pretty simple problem, what is the trouble you're having exactly? First solve for sin(theta), and then find all theta that satisfy that equation.

3. Sep 4, 2006

### arizona_cards_11

2sin^2 (theta) = 1

sin^2(theta) = 1/2

sin(theta) = sqrt(1/2

???? Those are my first few steps.....are there any problems?

4. Sep 4, 2006

### d_leet

Nope that is perfectly correct, now you just need to find the values of theta with sines of sqrt(1/2).

5. Sep 4, 2006

### arizona_cards_11

I don't have a calculator with me so I'll have to wait until school......

The next question using same directions:

tan^2(theta) - tan(theta) = 0

6. Sep 4, 2006

### d_leet

You might notice that this is a quadratic equation in tan(theta) so let x=tan(theta) and solve the resulting quadratic equation. Then you will have 2 equations to solve for tan(theta).

7. Sep 4, 2006

### arizona_cards_11

okay....

x^2 - x = 0

(x-1)(x+0) = 0

x = 1 or x = 0

8. Sep 4, 2006

### arizona_cards_11

Am I on the right track here???

9. Sep 4, 2006

### d_leet

Yep so now you can substitute x=tan(theta) back in and find the values of theta such that those equations are satisfied.

10. Sep 4, 2006

### arizona_cards_11

I'm a little bit confused on this point.....

I plug tan(theta) back into (x-1)(x+0) ?

Thus, making..... tan(theta) = 1 and tan(theta) = 0

11. Sep 4, 2006

### d_leet

No you had x=1 or x=0, from there put x=tan(theta) and then find teh values of theta that will satisfy that.

12. Sep 4, 2006

### arizona_cards_11

Is there any way to show your work besides plugging in....as my teacher is a stickler for descriptive work?

13. Sep 4, 2006

### d_leet

Well I'm not really sure there are many wasy to show your work for this kind of a problem, but once you have it down to solving for theta, if you've memorized the important angles then it should be pretty simple to find what angles satisfy these conditions and then just explain that these are the angles satisfying the equations.

14. Sep 4, 2006

### arizona_cards_11

The answers in the book are.....

0 , (pi/4) , pi , ((5pi)/(4))

15. Sep 5, 2006

### HallsofIvy

Staff Emeritus
You are clearly expected to know the trig functions for some basic angles, not just use a calculator.

16. Sep 5, 2006

### navneet1990

hey this stuff is easy
cant we use the identities
like

cos ( A-B) = cosA.cosB + sinA.sinB
and the other identities???

17. Sep 5, 2006

### shmoe

If sin^2(theta)=1/2 then you should have two possibilities for sin(theta), not just the one you have.