For what value of x is sin x = cos 19°, where 0°< x < 90°? 38°

x = 71.

Step-by-step explanation:

Given  : sin x = cos 19°, where 0°< x < 90°.

To find : For what value of x .

Solution : We have given

sin x = cos 19°.

By the trigonometric rule sin x = cos ( 90 -x ).

We can write cos ( 90 -x ) in place of sin x.

cos ( 90 -x ) = cos 19°.

Then

90 - x = 19 .

On subtracting both sides by 90

-x = 19 -90 .

- x = -71.

On dividing by -1

x = 71.

Therefore, x = 71.