## itsmichelle29 one year ago Simplify root(1-sintheta)(1+sintheta)

1. anonymous

$\sqrt{(1-sin{\theta})(1+sin{\theta})}$ ?

2. anonymous

Is that what you meant?

3. itsmichelle29

Yup

4. itsmichelle29

±sin θ cos θ ±tan θ square root sine theta

5. itsmichelle29

those are the answerscan u help me

6. anonymous

$$\sqrt{(1-sin{\theta})(1+sin{\theta})}$$ $$\sqrt{(1-sin^2{\theta })}$$ But $$cos^2{\theta} + sin^2{\theta} = 1$$, then $$\sqrt{cos^2{\theta}}$$ $$\pm cos{\theta}$$

7. itsmichelle29

so would the answer be costheta only

8. anonymous

yes

9. itsmichelle29

omg thank you can u help me with one more only

10. anonymous

sure^^

11. itsmichelle29

12. itsmichelle29

@M4thM1nd

13. anonymous

$$cos(x-\pi/2) = sin(x)$$ and $$sin(x - \pi/2)=-cos(x)$$

14. anonymous

So, which one you think is the right answer?

15. itsmichelle29

1st one

16. itsmichelle29

i think ... idk

17. anonymous

No. From the graph we see that f(x) at x = 0 is 0, that means f(x) is some function of sin(x), since sin(x) at x = 0 is 0

18. itsmichelle29

19. anonymous

In that case, the first one we have $$sin(x-\pi/2) = -cos(x)$$, so that can't be the right answer

20. itsmichelle29

okay the right answer is ...

21. anonymous

If we check the last option, we have $$cos(x-\pi/2) = sin(x)$$, but from the graph we also get the information that f(x) at x = pi/2 is equal to -4. But sin(x) at x = pi/2 is equal to 1. That tells us that we need a -4 multiplying this sin(x). So... The last option is the correct answer

22. anonymous

do you understand?