Question

If sin d° = 0.25 and sin k° = 0.75, which of the following is the value of cos d° + cos k°?

A. 1.68
B. 1.59
C. 1.61
D. 1.63

Answer 1

Task. If $\sin d=0.25$ and $\sin k=0.75$, which of the following is the value of $\cos d+\cos k$?

A. $1.68$

B. $1.59$

C. $1.61$

D. $1.63$

Solution. Since

$\sin^{2}x+\cos^{2}x=1$

for all $x$, we have that

$\cos x=\pm\sqrt{1-\sin^{2}x}.$

Since all variants A.-D. are greater 1, assume that $\cos d>0$ and $\cos k>0$.

Then

$\cos d=\sqrt{1-\sin^{2}d}=\sqrt{1-0.25^{2}}=\sqrt{0.9375}\approx 0.96825,$

and

$\cos k=\sqrt{1-\sin^{2}k}=\sqrt{1-0.75^{2}}=\sqrt{0.4375}\approx 0.66144.$

Therefore

$\cos d+\cos k\approx 0.96825+0.66144=1.6297\approx 1.63.$

Answer. D) $\cos d+\cos k\approx 1.63.$