Trigonometry Worksheet (Page 2 of 22) in pdf

Trigonometry Worksheet Page 2

Example 1: State the angle measurement in degrees for the following angles.

1. Initial side: positive x-axis, terminal side: negative y-axis, counter-clockwise rotation.

2. Initial side: positive y-axis, terminal side: positive x-axis, clockwise rotation.

3. Initial side: negative x-axis, terminal side: negative y-axis, counter-clockwise rotation.

4. Initial side: positive y-axis, terminal side: negative x-axis, clockwise rotation

Solution:

1. 270°

2. –90°

3. 90°

4. –270°

Some angles have special names: an angle of 180° is called a straight angle, and an angle of 90° is called a

right angle. Angles between 90° and 180° are called obtuse and angles between 0° and 90° are called acute.

When two angles sum to 180°, they are called supplementary. When two angles sum to 90°, they are called

complementary. (See Fig 3).

Fig 3

When two angles have the same initial and terminal sides, they are called coterminal. In fact, every angle

has an infinite number of equivalent coterminal angles, since we may allow the ray to rotate many times

about the plane, in either the positive or negative directions. For example, if a ray rotates

counterclockwise from the positive x-axis to the positive y-axis, it forms an angle of 90°. Equivalently, in

the clockwise direction, this angle has a measure of –270°. These two angles are coterminal; see Fig. 4:

Fig. 4

If the ray was allowed to rotate more than once before ending at its terminal side, other coterminal angle

measures would be 450°, 810° and 1170° (one, two and three complete extra revolutions in the positive

Trigonometry Worksheet Page 2