Trigonometry (Any Angle)

Michigan State University - Diagnostic Exam

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6.18

Find $a = cosθ$ and $b = sin θ$ where $θ$ is the angle shown in the sketch below.

a) $√ -- a = - 3, b = 1$ b) $√-- 1 3 a = -, b = ---- 2 2$ c) $√-- 3 1 a = ---, b =-- 2 2$

d) $- √3-- 1 a = -----, b = -- 2 2$ e) $1 - √3-- a = --, b =----- 2 2$

Solution:

Notice that the distance from the origin to $√ -- (- 3, 1)$ (shown in red) has length $∘ (√--)2----- 3 + 12 = 2$ . It follows that

√ -- ----3 1- a = cos θ = 2 and b = sinθ = 2

Diagnostic:

If you miss this question please review trigonometric functions of any angle.

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July 15, 2008