Question

score: 12/27 answered: 10/22
question 11
suppose ( a = 315 ^ { circ } ). then ( a ) is an angle in quadrant
i
ii
iii
iv
the reference angle for ( a ) is

Explanation:

Step1: Determine the quadrant

Quadrant I: \(0^{\circ}<\theta <90^{\circ}\)
Quadrant II: \(90^{\circ}<\theta <180^{\circ}\)
Quadrant III: \(180^{\circ}<\theta <270^{\circ}\)
Quadrant IV: \(270^{\circ}<\theta <360^{\circ}\)
Since \(270^{\circ}<315^{\circ}<360^{\circ}\), \(A = 315^{\circ}\) is in Quadrant IV.

Step2: Calculate the reference angle

The formula for the reference angle \(\alpha\) of an angle \(\theta\) in Quadrant IV is \(\alpha=360^{\circ}-\theta\)
Substitute \(\theta = 315^{\circ}\) into the formula: \(\alpha=360^{\circ}-315^{\circ}=45^{\circ}\)

Answer:

IV. The reference angle for \(A\) is \(45^{\circ}\)