Use the Fundamental Identities to Find the Value of the Trigonometric

Multiple Choice

Use the fundamental identities to find the value of the trigonometric function.
-An alien observer on Planet X can approximate distances in the sky by using his "hand" at arm's length. An outstretched hand is about 35 arc degrees, a clenched fist is about 25 arc degrees, and a
Thumb corresponds to about 1 arc degree. (i) If one clenched fist plus one outstretched hand covers
The distance between two stars, about how far apart in arc degrees are the stars? (ii) The apparent
Size of Moon X as observed from Planet X is about 21 arc minutes. Approximately what part of an
Observer's thumb would cover Moon X?

A) (i) 26 arc degrees; (ii) approximately $\frac { 1 } { 2 }$ of a thumb
B) (i) 60 arc degrees; (ii) approximately $\frac { 1 } { 3 }$ of a thumb
C) (i) 50 arc degrees; (ii) approximately $\frac { 1 } { 4 }$ of a thumb
D) (i) 61 arc degrees; (ii) approximately $\frac { 1 } { 5 }$ of a thumb