Question

If sin x is approximately .3420, what is the measurement of x to the nearest degree?

Approximately what is the cosine of the angle that is complementary to x

A. 70; 0.9397
B.70; 0.3420
C. 20;9397
D.20;3420

Answer 1

Part 1)
`x=20\°`

Part 2) 0.3420

Option D. 20;3420

Explanation:

step 1

Find the measurement of angle x

we know that

`sin(x)=0.3420`

Using a calculator

`x=sin^(1)(0.3420)=20\°`

step 2

Find the angle complementary to angle x

Remember that

If two angles are complementary, then their sum is equal to 90 degrees

Let

y ----> measure of angle complementary to angle x

so

`x+y=90\°`

we have

`x=20\°`

substitute

`20\°+y=90\°`

`y=90\°-20\°=70\°`

we know that

If two angles are complementary, then the sine of first angle is equal to the cosine of the second angle, or the sine of second angle is equal to the cosine of the first angle

so

if

`x+y=90\°`

then

cos(y)=sin(x)

substitute

`cos(70\°)=sin(20\°)=0.3420`