Question

Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.

Answer 1

ANSWER

$\sin( \theta) = - \frac{15}{17}$

$\csc( \theta) = - \frac{17}{15}$

$\cos( \theta) = \frac{8}{17}$

$\sec( \theta) = \frac{17}{8}$

$\tan( \theta) = - \frac{15}{8}$

$\cot( \theta) = - \frac{8}{15}$

EXPLANATION

From the Pythagoras Theorem, the hypotenuse can be found.

${h}^{2} = 1 {5}^{2} + {8}^{2}$

${h}^{2} = 289$

$h = \sqrt{289}$

$h = 17$

The sine ratio is negative in the fourth quadrant.

$\sin( \theta) = - \frac{opposite}{hypotenuse}$

$\sin( \theta) = - \frac{15}{17}$

The cosecant ratio is the reciprocal of the sine ratio.

$\csc( \theta) = - \frac{17}{15}$

The cosine ratio is positive in the fourth quadrant.

$\cos( \theta) = \frac{adjacent}{hypotenuse}$

$\cos( \theta) = \frac{8}{17}$

The secant ratio is the reciprocal of the cosine ratio.

$\sec( \theta) = \frac{17}{8}$

The tangent ratio is negative in the fourth quadrant.

$\tan( \theta) = - \frac{opposite}{adjacent}$

$\tan( \theta) = - \frac{15}{8}$

The reciprocal of the tangent ratio is the cotangent ratio

$\cot( \theta) = - \frac{8}{15}$

Answer 2

Answer:

sin=-15/17

cos=8/7

tan=-15/8

csc=-17/15

sec=17/8

cot=-8/15