trigonometry

Question

 Evaluate: Tan ( sin-1 1/2)

Answer 1

Don't forget to put your answer in a form that contains no radicals in the denominator:

 

1/√3 *√3/√3 = (√3)/3

Answer 2

Follow this link to a picture of a 30-60-90^o right triangle:

 

http://www.biology.arizona.edu/biomath/tutorials/trigonometric/graphics/trig_30_60_90.gif

 

From the picture, you can see that sin(30^o) = 1/2.  Therefore, sin^-1(1/2) = 30^o.

Hence tan(sin^-1(1/2)) = tan(30^o).  From the picture again, we can see that tan(30^o) = 1/√3