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# Determining the exact value of each trig expression

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4 I need to determine the exact value for cos 195°. The answer is $${- \sqrt{3} + 1 \over \sqrt{3}+1}$$ or $${\sqrt{3} - 2}$$ in the textbook, what did I do wrong?

Thank you! :)

Feb 21, 2019

#1
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Determining the exact value of each trig expression.

$$\cos(195^\circ)=-\cos(15°) = -\dfrac14 *\sqrt{2}*(\sqrt{3}+1) \\ \tan(165^\circ)=-\tan(15°) = \sqrt{3} - 2$$ Feb 21, 2019
#2
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Also, I'm a little confused about the method you've used.

Guest Feb 21, 2019
#4
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Hi Guest,

$$\begin{array}{|rcll|} \hline && \mathbf{\cos(195^\circ)} \\ &=& \cos(180^\circ +15^\circ)\\ &=& \underbrace{\cos(180^\circ)}_{=-1}\cos(15^\circ) - \underbrace{\sin(180^\circ)}_{=0}\sin(15^\circ)\\ &=& -\cos(15^\circ) - 0\cdot \sin(15^\circ)\\ &\mathbf{=}& \mathbf{-\cos(15^\circ)} \\\\ &=& -\cos(45^\circ - 30^\circ) \\ &=& -\Big( \underbrace{\cos(45^\circ)}_{=\dfrac{\sqrt{2}}{2}} \underbrace{\cos(30^\circ) }_{=\dfrac{\sqrt{3}}{2}} + \underbrace{\sin(45^\circ)}_{=\dfrac{\sqrt{2}}{2}} \underbrace{\sin(30^\circ)}_{=\dfrac{1}{2}}\Big) \\ &=& -\dfrac14 *\sqrt{2}*(\sqrt{3}+1) \\ \hline \end{array}$$ heureka  Feb 22, 2019
edited by heureka  Feb 22, 2019
#3
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cos (195)  =

cos (135 + 60) =

cos135cos60 - sin135sin60 =

-√2/2 * 1/2  -  √2/2 * √3/2    =

-√2/4 - √6/4 =

- [ √2 + √6 ] / 4  =

-√2 [ 1 + √ 3 ] /  4   Feb 21, 2019
edited by CPhill  Feb 21, 2019