# Math Help - sin(x)=1/3. What is cos(x?)

1. ## sin(x)=1/3. What is cos(x?)

Given that $\sin \theta = \frac{1}{3}$, how does one find the exact value of $\cos \theta$ without using a calculator?

The answer is supposed to be $\cos \theta = \frac{2\sqrt{2}}{3}$, but I don't see how one reaches it. I know the standard sine/cosine angles ( $\frac{\pi}{2}, \frac{\pi}{3}, \frac{\pi}{4}$...) and their corresponding Cartesian coordinates on the unit circle; is the result supposed to be derived from these? If so, how?

2. Draw a right angled triangle.

Let theta be an angle, 1 will be the opposite side, and 3 will be the hypotenuse.

Can you find the adjacent side through Pythagoras' Theorem?

Then, cos of theta is adj/hyp.

3. Use the Pythagorean Identity $\displaystyle \sin^2{\theta} + \cos^2{\theta} \equiv 1$.

4. Originally Posted by Unknown008
Draw a right angled triangle.

Let theta be an angle, 1 will be the opposite side, and 3 will be the hypotenuse.

Can you find the adjacent side through Pythagoras' Theorem?

Then, cos of theta is adj/hyp.

6. Well, you should know that $sin^2 x+cos^2x=1$. You know $sin \theta$, $cos^2 \theta$ is... ?
What do you know about $\theta$? In which interval is it and how is cos function on that interval (positive or negative)?