Question

If the sine of an angle is 4/7 what is the cosine of its complement.

Answer 1

Answer: 0.57

Explanation:

Let's begin by explaining that two angles are complementary when they sum is $90\°$:

$\theta + \alpha=90\°$

Having this clear, let's find $\theta$ from the following trigonometric function:

$sin \theta=\frac{4}{7}$

$\theta=sin^{-1} (\frac{4}{7})=34.84 \°$

Now that we have the value of $\theta$, let's find $\alpha$:

$\alpha=90\°-\theta$

$\alpha=90\°-34.84 \°$

$\alpha=55.15\°$ This is the complement of angle $\theta$

Then, the cosine of the complement $\alpha$ is:

$cos \alpha=cos(55.15\°)$

$cos \alpha=0.57$ This is the answer