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Calculate \cos \theta\ and\ \sin \theta\ for\ \theta= 150^\circ. Leave your answer in exact form.

Question:

Calculate {eq}\cos \theta\ and\ \sin \theta\ for\ \theta= 150^\circ. {/eq} Leave your answer in exact form.

Use of Trigonometric Functions:

The trigonometric function are used to describe the relation between one angle of the triangle and two sides of the triangle. The example of the trigonometric function are as follows sine of an angle, cosine of an angle and tangent of an angle.

Answer and Explanation:


Given Data

  • The value for {eq}\theta {/eq} is {eq}\theta = 150^\circ {/eq}.


The expression for the sine is,

{eq}\begin{align*} \sin 150^\circ &= \sin \left( {90 + 60} \right)^\circ \\ &= \cos 60^\circ \\ &= \dfrac{1 }{{ 2 }} \end{align*} {/eq}


Thus, the exact value for the {eq}\sin 150^\circ {/eq} is {eq}\dfrac{1 }{{ 2 }} {/eq}.


The expression for the cosine is,

{eq}\begin{align*} \cos 150^\circ &= \cos \left( {90 + 60} \right)^\circ \\ &= - \sin 60^\circ \\ &= - \dfrac{\sqrt 3}{{ 2 }} \end{align*} {/eq}


Thus, the exact value for the {eq}\cos 150^\circ {/eq} is {eq}- \dfrac{\sqrt 3}{{ 2 }} {/eq}.


Learn more about this topic:

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Trigonometric Functions: Definition & Examples

from Calculus: Help and Review

Chapter 3 / Lesson 6
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