How do you evaluate sin(5(pi)/4) - cos(11(pi)/6)?

1 Answer
Mia
Oct 23, 2016

-(sqrt2+sqrt3)/2

Explanation:

In this exercise we will use the following trigonometric identities:

color(purple)(sin(pi+alpha)=-sinalpha)
color(blue)(cos(-alpha)=cosalpha)

sin((5pi)/4)-cos((11pi)/6)
=sin((4pi+pi)/4)-cos((12pi-pi)/6)
=sin((4pi)/4+pi/4)-cos((12pi)/6-pi/6)
=sin(pi+pi/4)-cos(2pi-pi/6)
=color(purple)(-sin(pi/4)-cos(-pi/6)
=color(purple)(-sin(pi/4)-color(blue)(cos(pi/6)
=-sin(pi/4)-cos(pi/6)
=-sqrt2/2-sqrt3/2
=-(sqrt2+sqrt3)/2

Related questions
See all questions in Trigonometric Functions of Any Angle
Impact of this question
4532 views around the world
You can reuse this answer
Creative Commons License