Question

Find a positive angle and a negative angle coterminal to π/4.

a) Positive angle: π/4, Negative angle: -7π/4
b) Positive angle: 9π/4, Negative angle: -π/4
c) Positive angle: 3π/4, Negative angle: -5π/4
d) Positive angle: 7π/4, Negative angle: -3π/4

Answer 1

To find coterminal angles, we add or subtract multiples of 2π (the circle's circumference) to the given angle. The positive angle coterminal to π/4 is π/4 + 2π = 9π/4, and the negative coterminal angle is π/4 - 2π = -7π/4. The correct answer is (a).

Step-by-step explanation:

To find a positive angle and a negative angle coterminal to π/4, we need to add or subtract multiples of 2π (the full circumference of the unit circle) since coterminal angles are angles that share the same initial and terminal sides but differ by full rotations. For the positive coterminal angle, we can simply add 2π since we are looking for a coterminal angle that is positive and larger than π/4:

• Positive angle coterminal to π/4: π/4 + 2π = 9π/4

For the negative coterminal angle, we need to subtract 2π from π/4 to get a negative result:

• Negative angle coterminal to π/4: π/4 - 2π = -7π/4

The correct answer is a) Positive angle: π/4, Negative angle: -7π/4.