Question

If the sin 90° = 1, then which statement is true? a. cos 0° = 1, because the cosine and sine are complements b. cos 90° = 1, because the cosine and sine are supplements c. cos 0° = 0, because the cosine and sine are complements d. cos 90° = 0, because the cosine and sine are supplements

Answer 1

Answer: c. cos 0° = 0, because the cosine and sine are complements

Step-by-step explanation:

• The sine of any acute angle is equal to the cosine of its complement.

$\sin x =\cos(90^{\circ}-x)$

• Similarly, The cosine of any acute angle is equal to the sine of its complement.

$\cos x=\sin (90^{\circ}-x)$

Given, $\sin 90^{\circ} = 1$

$\Rightarrow\cos(90^{\circ}-90^{\circ}=1) [\because \sin x =\cos(90^{\circ}-x)]$

$\Rigghtarrow\ \cos0^{\circ}=1$

Hence, the correct statement is c. cos 0° = 0, because the cosine and sine are complements.