Question

Calculate the value of $\cos \left({60}^{\circ }{5}^{\prime }\right)$.

• A. 0.498
• B. 0.497
• C. 0.496
• D. 0.948

Answer 1

Answer: (A)

0.498

$\cos \left({60}^{\circ }{5}^{\prime }\right)$

$=\cos ({60}^{\circ }+5^{\prime })$

Using compound angle formula,$\cos (A+B)=\cos A\cos B-\sin A\sin B$

$=\cos {60}^{\circ }\cos 5^{\prime }-\sin {60}^{\circ }\sin 5^{\prime }$

$=\frac{1}{2}\times \cos {\frac{5}{60}}^{\circ }-\frac{\sqrt{3}}{2}\times \sin {\frac{5}{60}}^{\circ }$

$=\frac{1}{2}\times \cos {0.0833}^{\circ }-\frac{\sqrt{3}}{2}\times \sin {0.0833}^{\circ }$

$=0.5\times 0.999998-0.866\times 0.00145=0.499999‬-0.0012557‬\approx 0.4987$