How To Find The Value Of A Trig Function

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The unit of measurement circumvolve is an first-class guide for memorizing common trigonometric values. Notwithstanding, there are often angles that are not typically memorized. We will thus demand to use trigonometric identities in social club to rewrite the expression in terms of angles that we know.

Preliminaries

In this article, nosotros will be using the post-obit trigonometric identities. Other identities tin be found online or in textbooks.
Summation/difference
One-half-bending

Steps

one

Review the unit circle. ^[1] If you lot are non strong with the unit circumvolve, it is important that you memorize the angles and understand for what quadrants are sine, cosine, and tangent positive and negative.

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one
Evaluate the following. The angle ${\frac {\pi }{12}}$ is not commonly found as an angle to memorize the sine and cosine of on the unit circle.
- $\cos {\frac {\pi }{12}}$
2
3
Use the sum/difference identity to separate the angles. ^[three]
- $\cos \left({\frac {\pi }{3}}-{\frac {\pi }{4}}\right)=\cos {\frac {\pi }{three}}\cos {\frac {\pi }{iv}}+\sin {\frac {\pi }{3}}\sin {\frac {\pi }{4}}$
iv
Evaluate and simplify.
- ${\frac {1}{2}}\cdot {\frac {\sqrt {2}}{2}}+{\frac {\sqrt {3}}{2}}\cdot {\frac {\sqrt {2}}{two}}={\frac {{\sqrt {two}}+{\sqrt {half dozen}}}{4}}$
Advertizing

1
Evaluate the following.
- $\sin {\frac {\pi }{8}}$
2
3
Apply the one-half-angle identity. ^[5]
- $\sin \left({\frac {ane}{2}}\cdot {\frac {\pi }{4}}\correct)=\pm {\sqrt {\frac {i-\cos {\frac {\pi }{4}}}{2}}}$
4
Evaluate and simplify. The plus-minus on the square root allows for ambiguity in terms of which quadrant the angle is in. Since ${\frac {\pi }{8}}$ is in the first quadrant, the sine of that angle must be positive.
- ${\sqrt {\frac {1-\cos {\frac {\pi }{4}}}{two}}}={\frac {\sqrt {two-{\sqrt {2}}}}{2}}$
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Question

How do I find the exact value of sine 600?

600° = lx° when considering trig functions. [600 - (iii)(180) = 60] Sine 600° = sine 60° = 0.866.
Question

What does ASTC stand for in trigonometry?

It stands for the "all sine tangent cosine" rule. Information technology is intended to remind u.s.a. that all trig ratios are positive in the first quadrant of a graph; only the sine and cosecant are positive in the second quadrant; only the tangent and cotangent are positive in the third quadrant; and only the cosine and secant are positive in the fourth quadrant.
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What's the exact value of cosecant 135?

You can find exact trig functions past typing in (for example) "cosecant 135 degrees" into whatsoever search engine.