Question

write and that is equivalent to each of the following expression,using the related acute angle
a) sin 13pi/6 b) cos 11pi/8
c) tan 7pi/4

Answer 1

a) sin(13π/6)
= sin(2π + π/6)
so we are in quadrant I with an angle of sin π/6
sin π/6 = 1/2

cos(11π/6)
= cos(2π-π/6) .... ( think: 330° = 360° - 30°)
so we are in quad IV and in IV the cosine is positive

= cos π/6 = √3/2

c) tan 7π/4
= tan (2π - π/4) ------ in IV where the tangent is negative
= -tan π/4 = -1

You can and should check your answers with a calculator.