Working with sin, cos and tan.

Question

If $\sin \theta = \frac 56$, what are the values of $\cos \theta$ and $\tan \theta$? I'm have a hard time knowing how to figure out this problem.

Answer 1

Hint

$$ \sin^2 \theta + \cos^2 \theta = 1 $$

$$ \tan \theta = \frac{\sin \theta}{\cos \theta} $$

You will have to assume $\sin$ and $\cos$ are positive; else there are two possibilities for $\cos$ and $\tan$ and no way to tell which is correct.

Answer 2

Use $\sin^2 \theta + \cos^2 \theta=1$ to get $\pm\cos \theta$ and $\tan \theta = \frac{\sin \theta}{\cos \theta}$...

Answer 3

Imagine a triangle. Pick one of the angles to consider $\theta$ and then label the lengths of the sides of the triangle. You can then easily find $\cos \theta, \tan \theta$ by using soh-cah-toa.

Picture:

Answer 4

$$\sin\theta=\frac{5}{6}$$ So,$$\cos\theta=\sqrt{1-\sin^2\theta}$$ $$\cos\theta=\sqrt{1-\frac{25}{36}}$$ $$\cos\theta=\frac{\sqrt{11}}{6}$$ And,$$\tan\theta=\frac{\sin\theta}{\cos\theta}$$ $$\tan\theta=\frac{\frac{5}{6}}{\frac{\sqrt{11}}{6}}$$ $$\tan\theta=\frac{5}{\sqrt{11}}$$ This is very simple.