Which of the following is the least? sin 3 (b) sin 2 (c) sin 1 (d) sin 7

Options

A. sin 3
B. sin 2
C. sin 1
D. sin 7

Answer

D

Explanation

(d) `sin3=sin[pi-(pi-3)]=sin(pi-3)=sin(0.14)`
`sin2=sin[pi-(pi-2)]=sin(pi-2)=sin(1.14)`
`sin7=sin[2pi-(7-2pi)]=sin(7-2pi)=sin(0.72)`
Now, `1.14gt1gt0.72gt0.14`
`rArr sin(1.14)gtsin1gtsin(0.72)gtsin(0.14)`
[as 1.14,1,0.72, 0.14 lie in the first quadrant and sine functions increase in the first quadrant]
Hence, among the given values, sin3 is the least.
Alternate solution:
We draw the graph of `y=sinx` abd compare the height of graph for different angles.

Form the graph, clearly sin 3 is the least as height of graph is the least for angle '3' radians.