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Q.

Find the reference angle for 108°.


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a

ρ=50°

b

ρ=60°

c

ρ=72°

d

ρ=40° 

answer is C.

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Detailed Solution

We try to break the angles inside 360° into the four normal quadrants. There are 4 quadrants - first, second, third, fourth. Now for any kind of given angle αα, the reference angle ρ will be the acute angle that the terminal side of the angle α makes with the x-axis.
These angles generally have non-quadrantal angles in normal positions. We always need to find the difference between the angle and the positive or negative x-axis.
Now we express the quadrant with different results.
For given angle α in the first quadrant (0°<α<90°), the reference angle will be ρ=α.
For given angle α in the second quadrant (90°<α<180°), the reference angle will be ρ=180°−α=π−α.
For given angle αα in the third quadrant (180°<α<270°), the reference angle will be ρ=α−180°=α−π.
For given angle αα in the first quadrant (270°<α<360°), the reference angle will be ρ=360°−α=2π−α
ρ=360°−α=2π−α.
The representation will be of the form
 Question ImageFor the given problem we need to find a reference angle for 108∘.
The angle 108° is in the second quadrant as (90°<108°<180°).
So, using the formulas the reference angle will be π−108°=180°−108°=72°.
So, the correct answer is “Option 3”.
 
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