Question

Find the exact value of the expression.(Hint: Sketch a right triangle.)

sin(arctan 3/4)

Answer 1

Step 1:

The trigonometric function is .

Consider , then .

Definition of inverse tangent function :

If  then .

Draw the right angled triangle :

From Pythagorean theorem,

The square of the hypotenuse is equal to sum the squares of the other two sides.

From above figure .

.

Substitute in .

Properties of inverse trigonometric function: .

Solution :

.