Precalculus Review

Trigonometric functions on a coordinate system

In a coordinate system an angle $\theta$ with the terminal side

(a radian on the unit circle) starts from the first quadrant (i.e., the positive

- and

-axis), and moves counterclockwise from the point

when $\theta > 0$ .

$\includegraphics{lec09e.ps}$

The angle $\theta$ moves clockwise when $\theta < 0$ .

$\includegraphics{lec09f.ps}$

In the setting of coordinate system, the cosine and the sine functions are now defined for every positive and negative angle $\theta$ as

$\displaystyle \cos\theta =$ the

-coordinate of

; $\displaystyle \quad\quad \sin\theta =$ the

-coordinate of

. $\displaystyle$

In other words the point on the unit circle with the radian $\theta$ is given by $P = (\cos\theta,\: \sin\theta)$ . The other trigonometric functions follows as they are defined in Trigonometric functions.