Trigonometry Answers

Express each of the following as a single trigonometric ratio, and then evaluate

Use double angle formula

a) 2 sin pi over 12 cos Pi over 12
b) 2 sin 45 degree cos 45 degree
c) 2 tan 60 degree cos^2 60 degree

Express each of the following as single trigonometric ratio

Use double angle formula

a) 2 sin 5x cos 5x
b) cos^2 0 - sin ^2 0
c) 1- 2 sin^2 3x
d) 2 tan 4x / 1-tan^2 4x

Simplify the following expression

Cos ( x+ Pi over 3) - sin ( x + Pi over 6 )

If sinx = 4/5 and siny= -12/13 , 0<x<Pi over 2, 3pi over 2 < y < 2pi, evaluate

a) cos (x+y)
b) tan (x-y)

Use the appropriate compound angle formula to create an equivalent expression

a) cos ( x+3pi over 2 )
b) sin ( pi + x )

4. Use the appropriate compound angle formula to determine the exact value of each expression

a) sin ( pi + Pi over 6 )
b) tan ( Pi over 4 + Pi )
c) cos ( -Pi - pi over 4 )

Determine the exact value of each trigonometric ratio

a) sin 75 degree
b) tan 5pie over 12
c) sin -pie over 12

Express each angle as a compound angle, using a pair of angles from the special triangles

a) 75 degrees
b) pie over 12
c) 5 pie over 6

Rewrite each expression as a single trigonometric ratio, and then evaluate the ratio ( show full work )

1a) tan 170• - tan 110• / 1+ tan 170• tan 110•

b) cos 5pie/12 x cos pie over 12 + sin 5pie over 12 x sin pie over 12

Isosceles triangle is similar to the Isosceles spherical tringale? Justify the answer