Question

Use the half-angle formulas to determine the exact values of the sine, cosine, and tangent of the angle.

75^o

Answer 1

Step 1:

To find .

Using half angle formula .

Here, and .

is lies in first quadrant.

The positive square root is chosen because  is positive in first quadrant.

.

Step 2:

To find .

Using half angle formula .

Here, and .

is lies in first quadrant.

The positive square root is chosen because  is positive in first quadrant.

.

Step 3:

To find .

Using half angle formula .

Here, and .

is lies in first quadrant.

.

Solution:

.

.

.