Question

Find the value of cos(-1170°)​

Answer 1

Answer:

$\cos \left(-1170^{\circ \:}\right)=0$

Step-by-step explanation:

$\cos \left(-1170^{\circ \:}\right)$

$\gray{\mathrm{Use\:the\:following\:property:}\:\cos \left(-x\right)=\cos \left(x\right)}$

$\gray{\cos \left(-1170^{\circ \:}\right)=\cos \left(1170^{\circ \:}\right)}$

$=\cos \left(1170^{\circ \:}\right)$

$\black{\cos \left(1170^{\circ \:}\right)}$

$\gray{\mathrm{Rewrite\:the\:angles\:for}\:\cos \left(1170^{\circ \:}\right):}$

$\displaystyle\gray{\cos \left(1170^{\circ \:}\right)=\cos \left(\frac{12+1}{2}180^{\circ \:}\right)=\cos \left(\left(\frac{12}{2}+\frac{1}{2}\right)180^{\circ \:}\right)=\cos \left(360^{\circ \:}\cdot \:3+\frac{1}{2}180^{\circ \:}\right)}$

$\displaystyle=\cos \left(360^{\circ \:}3+\frac{1}{2}180^{\circ \:}\right)$

$\gray{\mathrm{Use\:the\:periodiciity\:of\:}\cos :\quad \cos \left(x+360^{\circ \:}\cdot \:k\right)=\cos \left(x\right)}$

$\displaystyle\gray{\cos \left(360^{\circ \:}\cdot \:3+\frac{1}{2}180^{\circ \:}\right)=\cos \left(\frac{1}{2}180^{\circ \:}\right)}$

$\displaystyle=\cos \left(\frac{1}{2}180^{\circ \:}\right)$

$\gray{\mathrm{Simplify}}$

$=\cos \left(90^{\circ \:}\right)$

$\gray{\mathrm{Use\:the\:following\:trivial\:identity}:\quad \cos \left(90^{\circ \:}\right)=0}$

$=0$