Question

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

Answer 1

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