Unit circle trigonometry

On a circle of radius $1$ centred at the origin, the point at angle $\theta$ has coordinates $(\cos\theta, \sin\theta)$. That single fact drives everything here.

Because the radius is $1$, cosine is simply the $x$-coordinate and sine the $y$-coordinate. So the sign of each is decided by the quadrant: both positive in the first, sine only in the second, both negative in the third, cosine only in the fourth.

Angles can be measured in degrees or radians, and converting between them uses $180^\circ = \pi$ radians. So $\frac{\pi}{3}$ is $60^\circ$ and $\frac{\pi}{2}$ is $90^\circ$.

Two relationships are worth knowing. The Pythagorean identity $\sin^2\theta + \cos^2\theta = 1$ follows directly from the circle's equation, and $\tan\theta = \frac{\sin\theta}{\cos\theta}$.

Most SAT questions here are conversions, quadrant-sign questions, or a single use of the identity — not heavy trigonometric manipulation.

Convert $\frac{\pi}{3}$ radians to degrees.
Use $\pi = 180^\circ$

If $\theta$ is in the second quadrant, what are the signs of $\sin\theta$ and $\cos\theta$?
The second quadrant has negative $x$ and positive $y$, so $\cos\theta < 0$ and $\sin\theta > 0$.

If $\sin\theta = 0.6$ and $\theta$ is in the first quadrant, find $\cos\theta$.
Apply the identity The first quadrant makes cosine positive, so $0.8$ rather than $-0.8$.