## Anikate one year ago how do u do this? cos2θ+cosθ=0 find solutions

1. Anikate

|dw:1434351527647:dw|

2. ganeshie8

As a start, factor out $$\large \cos\theta$$

3. Anikate

ok

4. Anikate

|dw:1434351738430:dw|

5. Anikate

@ganeshie8

6. ganeshie8

Ahh that is wrong, and don't wry thats a typical mistake committed by everyone in the start

7. Anikate

hmm lol

8. ganeshie8

$$\large \cos^2\theta$$ is same as $$\large (\cos \theta)^2$$

9. Anikate

ok

10. Anikate

lol idk how that helps

11. ganeshie8

when you factor out $$\cos\theta$$ from $$(\cos\theta)^2$$, there will be $$\cos\theta$$ left behind : |dw:1434352204156:dw|

12. Anikate

oooh

13. ganeshie8

next use zero product property if the product of two factors is 0, then at least one of the factors must be 0

14. Anikate

ok so the cos theta on the outside is = to 0

15. ganeshie8

|dw:1434352435421:dw|

16. Anikate

thats it?

17. ganeshie8

we need to find $$\theta$$ using unit circle

18. ganeshie8

for what values of $$\theta$$, the cos function becomes 0 ?

19. Anikate

umm...... 0 degrees?

20. ganeshie8

careful, do u have unit circle ?

21. Anikate

22. Anikate

lol

23. ganeshie8

Good

24. ganeshie8

The first coordinate represents the cosine value : |dw:1434352712518:dw|

25. Anikate

oh 1,0

26. ganeshie8

No, listen to my question again. For what values of $$\theta$$, the cosine function is 0 ?

27. Anikate

hey is 3:20am here, I can barely concentrate, can u please leave the work, and I'll check back in the morning? sorry and thanks for all ur help and co operation! :)

28. ganeshie8

Assuming we want to find the principle value, from the unit circle, $\cos\theta = 0 \implies \theta = 90,270$ $\cos\theta = -1 \implies \theta = 180$

29. ganeshie8

so $$\theta = 90,180,270$$ are the solutions