Find the exact value of sin(285^o).

Question:

Find the exact value of {eq}sin(285^o). {/eq}

ASTC Rule

The ASTC rule defines the values of sine, cosine, tangent, cotangent, etc. depending on the particular condition. In the first coordinate, all trigonometric functions are positive. In the second coordinate, sine and cosecant function will be positive. In the third coordinate, the tangent and cotangent function is positive. In the fourth coordinate, the cosine and secant function are positive.

Answer and Explanation:


Given data

  • The given sine function is: {eq}\sin \left( {285^\circ } \right) {/eq}


Solve the given value using ASTC rule,

{eq}\begin{align*} \sin \left( {285^\circ } \right) &= \sin \left( {270^\circ + 15^\circ } \right)\\ &= - \cos \left( {15^\circ } \right)\\ &= - 0.9659 \end{align*} {/eq}


Thus, the value of {eq}\sin \left( {285^\circ } \right) {/eq} is {eq}- 0.9659 {/eq}.


Learn more about this topic:

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How to Find the Period of Sine Functions

from High School Precalculus: Help and Review

Chapter 24 / Lesson 7
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