Question

how to find a reference angle for Θ=-155 degrees?

i have a test tomorrow and would prefer a walk through instead of a direct answer

Answer 1

Which quadrant is the angle in?

Answer 2

Two or more coterminal angles have the same reference angle.

Assume angle A is postive and less than 360 o (2Pi), we have 4 possible cases:

1. If angle A is in quadrant I then the reference angle
A r = A.

2. If angle A is in quadrant II then the reference angle
A r = 180 o - A if A is given degrees
and
A r = Pi - A if A is given in radians.

3. If angle A is in quadrant III then the reference angle
A r = A - 180 o if A is given degrees
and
A r = A - Pi if A is given in radians.

4. If angle A is in quadrant IV then the reference angle
A r = 360 o - A if A is given degrees
and
A r = 2Pi - A if A is given in radians.

Answer 3

**EXAMPLE**

Find the reference angle to angle A = 120 o.

Solution:

Angle A is in quadrant II and the reference angle is given by

A r = 180o - 120o = 60o

Answer 4

so, i add 360 to find the coterminal angle, which is 205 and in quadrant 3. so tinge it is quadrant 3 i take 205-180=25o? is that right?

Answer 5

Here is the simple way.
Graph the angle and figure out how many degrees it is from the x axis. That is the reference angle.

Answer 6

thanks!

Answer 7

99