Question

Let sin m = .11. Which of the following is sin m/2?

A. .79
B. .78
C. .77
D. .05

Answer 1

Task. Let $\sin m=0.11$. Which of the following is $\sin(m/2)$?

A. $0.79$

B. $0.78$

C. $0.77$

D. $0.05$

Solution. Notice that

$\cos m=\sqrt{1-\sin^{2}m}=\sqrt{1-0.11^{2}}=\sqrt{0.9879}\approx 0.99393$

and

$\cos^{2}(m/2)=\frac{1+\cos m}{2}=\frac{1+0.99393}{2}=0.996965.$

Therefore

$\sin(m/2)=\sqrt{1-\cos^{2}(m/2)}=\sqrt{1-0.996965}=\sqrt{0.003035}\approx 0.05.$

Thus the answer is D. $0.05$