## rox13kh 2 years ago sin0 + cos0 = 7/6 what is sin0 - cos0 = ? 0 represents theta

1. Hyun11

$2(\pi n+\arctan(\frac{1}{13}(6-\sqrt{23})))$

2. Hyun11

$n\in \mathbb{Z}$

3. Callisto

$sin\theta + cos\theta = \frac{7}{6}$$(sin\theta + cos\theta)^2 = (\frac{7}{6})^2$$sin^2\theta + cos^2\theta+2sin\theta cos\theta= \frac{49}{36}$$1+2sin\theta cos\theta= \frac{49}{36}$$2sin\theta cos\theta= \frac{13}{36}$ $sin\theta - cos\theta$$=\sqrt{(sin\theta - cos\theta)^2}$$=\sqrt{(sin^2\theta-2sin\theta\cos\theta+\cos^2\theta)}$You know what $$sin^2\theta + cos^2\theta$$ and $$2sin\theta\cos\theta$$ are, so you can find the answer.

4. Callisto

5. xlegendx
6. shubhamsrg

sin0 + cos0 = 7/6 let sin0 - cos0 = x square both sides of both eqns and add them, you'll get your answer in the very next step.

7. rox13kh

how if you are asked $(\sin \theta)^2 - (\cos \theta)^2$ ? @Callisto

8. myininaya

Do you know how to solve for sin(theta) and cos(theta) given the two equations above?

9. myininaya

a+b=7/6 a-b=(callisto basically gave you this answer) Solve the system of linear equations

10. myininaya

Plug into a^2-b^2 and you got it

11. rox13kh

thx, that helped a lot @myininaya

12. myininaya

np :)