If sin(x) = 1/8 and x is in quadrant I, find the exact values of the expressions without solving for x.

Question

If sin(x) = 1/8 and x is in quadrant I, find the exact values of the expressions without solving for x.

 

a) sin(2x)

b) cos(2x)

c) tan(2x)

Answer 1

sin(2x) = 2sin(x)cos(x)

 

cos(2x) = 1 - 2sin²(x)

 

tan(2x) = 2tan(x) / (1 - tan²x)

 

 

First, you need to find cos(x) before finding those 3 values using Pythagorean theorem.

 

cos(x) = √(1 - sin²(x))

 

 

You may also use the identity    tan(x) = sin(x) / cos(x)         for the last value.