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Use trigonometric identities to get the value of all 6 trigonometric functions of 165 degrees.

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4 Answers 4

Hint: $165=(180-30)+(30/2)$. $\ \ \ \ \ \!\!\!\!$

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Hint: $165=120+45$. ${}{}{}{}$

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Using All Sin Tan Cos formula,

$\sin(180^\circ-x)=\sin x,\cos(180^\circ-x)=-\cos x$ and $\tan(180^\circ-x)=-\tan x$

and $\sin(A-B)=\sin A\cos B-\cos A\sin B,$

$\cos(A-B)=\cos A\cos B+\sin A\sin B$

and $\tan(A-B)=\frac{\tan A-\tan B}{1+\tan Atan B}$

$\sin(165^\circ)=\sin(180^\circ-15^\circ)=\sin 15^\circ=\sin(60^\circ-45^\circ)$

$\cos(165^\circ)=\cos(180^\circ-15^\circ)=-\cos 15^\circ=-\cos(60^\circ-45^\circ)$

$\tan(165^\circ)=\tan(180^\circ-15^\circ)=-\tan 15^\circ=-\tan(60^\circ-45^\circ)$

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You can also do this for $15^\circ$. Once you get the value for the sine, the rest can be readily obtained. Use the fact that $45 - 30 = 15$.

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