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

Question

asked Feb 12, 2021 59.2k views

1 Answer

Zin Win Htet · Answer 1 · 2021-02-17T10:02:00+0000

Answer: 0.57

Step-by-step 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:

$sin \theta=(4)/(7)$

$\theta=sin^(-1) ((4)/(7))=34.84 \°$

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