## anonymous one year ago Solving Trigonometric Equations

1. freckles

post the equation when you are ready :)

2. anonymous

|dw:1436825812888:dw|

3. freckles

write in terms of just cos by using Pythagorean identity

4. anonymous

whats that?

5. freckles

you will have a quadratic equation in terms of cos(theta)

6. freckles

$\sin^2(\theta)+\cos^2(\theta)=1 \text{ is one of the pythagorean identities }$

7. freckles

$\sin^2(\theta)=1-\cos^2(\theta)$

8. freckles

$3(1-\cos^2(\theta))=1+\cos(\theta) \\ 3-3\cos^2(\theta)=1+\cos(\theta)$

9. freckles

if you want replace cos(theta) with u for now $3-3u^2=1+u$ solve for u

10. freckles

by first putting everything on one side

11. anonymous

but i have a range to follow

12. anonymous

and i got u=1

13. freckles

hmmm how did you get u=1?

14. freckles

$3-3u^2=1+u \\ \text{ add } 3u^2 \text{ and subtract } 3 \text{ on both sides } \\ 0=3u^2+u+1-3 \\ 0=3u^2+u-2 \\ 0=(3u-2)(u+1)$

15. freckles

neither u+1=0 or 3u-2=0 leads to u=1

16. freckles

but anyways you have the following equations to solve recall we replaced cos(theta) with u so we actually have $\cos(\theta)+1=0 \text{ or } 3\cos(\theta)-2=0$ you need to solve these two equations for theta