Question

Use the figures to evaluate the function if f (x) = sin x, g (x) = cos x,  and h (x) = tan x.

f (α + β)

Answer 1

Step 1:

The functions are .

Find .

From trigonometric identities : .

Step 2:

From figure (1),

The circle is and point is .

Rewrite the equation.

.

It is in the form of .

Then .

Substitute the point in a circle equation.

Observe figure(1) :

.

.

lies in quadrant I.

.

.

Step 3:

From figure (2),

The circle is and point is .

Rewrite the equation.

.

It is in the form of .

Then .

Substitute the point in a circle equation.

Observe figure(1) :

The point lies in quadrant IV, then

.

.

As lies in quadrant IV.

.

.

Step 4:

Substitute the values of in equation.

.

Solution :

.