Question

find the reference angle for the given angle. (a) 120° (b) -240° (c) 765° resources read it

Explanation:

Step1: Identify quadrant for 120°

120° is in 2nd quadrant.

Step2: Calculate reference angle for 120°

$180 - 120=60$

Step3: Adjust - 240° to positive angle

$-240^{\circ}+360^{\circ}=120^{\circ}$, which is in 2nd quadrant.

Step4: Calculate reference angle for - 240°

$180 - 120 = 60$

Step5: Reduce 765° to equivalent angle

$765^{\circ}\div360^{\circ}=2\cdots\cdots45^{\circ}$, so 765° is coterminal with 45° which is in 1st quadrant.

Step6: Calculate reference angle for 765°

Since in 1st quadrant, reference angle is itself, so it's 45.

Answer:

(a) 60
(b) 60
(c) 45