Trigonometric Identities Question 139
Question: The difference of two angles is $ 1{}^\circ ; $ the circular measure of their sum is 1. What is the smaller angle in circular measure?
Options:
A) $ [ \frac{180}{\pi }-1 ] $
B) $ [ 1-\frac{\pi }{180} ] $
C) $ \frac{1}{2}[ 1-\frac{\pi }{180} ] $
D) $ \frac{1}{2}[ \frac{180}{\pi }-1 ] $
Show Answer
Answer:
Correct Answer: C
Solution:
Let the angles are $ \alpha $ and $ \beta , $ then $ \alpha -\beta =1{}^\circ $
$ \Rightarrow \alpha -\beta =\frac{\pi }{180{}^\circ } $ is circular measure .. .(i) As given, $ \alpha +\beta =1 $ …(ii) On solving Eqs. (i) and (ii), we get, $ \alpha =\frac{1}{2}[ 1+\frac{\pi }{180{}^\circ } ] $ and $ \beta =\frac{1}{2}[ 1-\frac{\pi }{180{}^\circ } ] $ $ \beta $ is the smaller angle. Hence, smaller angle $ =\frac{1}{2}[ 1-\frac{\pi }{180{}^\circ } ] $
BETA
