How do you find the exact functional value cos(285 degrees) using the cosine sum or difference identity?

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How do you find the exact functional value cos(285 degrees) using the cosine sum or difference identity?

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Answer 1 · 2015-09-23T04:26:17

Find cos (285) deg

Ans: $(\frac{\sqrt{2}}{4}) (\sqrt{3} - 1)$ $(sqrt2/4)(sqrt3 - 1)$

Explanation:

cos (285) = cos (135 + 150)
Apply the trig identity: cos (a + b) = cos a.cos b - sin a.sin b
Use the Trig Table of Special Arcs.
Call a = 135 --> $sin a = \frac{\sqrt{2}}{2}$ $sin a = sqrt2/2$ and $cos a = - \frac{\sqrt{2}}{2}$ $cos a = -sqrt2/2$
Cal b = 150 --> $sin b = \frac{1}{2}$ $sin b = 1/2$ and $cos b = - \frac{\sqrt{3}}{2} .$ $cos b = -sqrt3/2.$
We get:
$cos (285) = \frac{(\sqrt{2}) (\sqrt{3})}{4} - \frac{\sqrt{2}}{4} = \frac{\sqrt{2}}{4} (\sqrt{3} - 1)$ $cos (285) = ((sqrt2)(sqrt3))/4 - sqrt2/4 = sqrt2/4(sqrt3 - 1)$

Check by calculator:
cos 285 = 0.26
$(\frac{\sqrt{2}}{4}) (\sqrt{3} - 1) = \frac{(0.73) (1.41)}{4} = 0.26 .$ $(sqrt2/4)(sqrt3 - 1) = ((0.73)(1.41))/4 = 0.26.$ OK

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How do you find the exact functional value cos(285 degrees) using the cosine sum or difference identity?

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