- #1
reventon_703
- 15
- 0
Homework Statement
Write the following in terms of the cofunction identity:
cos(4pi/3)
Homework Equations
I know the θ is in Quadrant 3, but my question is, which cofunction identity am I suppose to use?
Cofunction Identities:
cosx = sin(pi/2 - x) #1
cosx = sin(pi/2 + x) #2
cos(pi + x) = -cosx
cosx = -cos(pi + x) #3
cos(pi - x) = -cosx
cosx = -cos(pi - x) #4
Is #2 only applicable for angles in quadrant 2 in terms of cofunction identity? But I tried using it and it still gave me the trig ratio. So what is the difference?
The Attempt at a Solution
#1 cos(4pi/3) = sin(pi/2 - 4pi/3) = -0.5
#2 cos(4pi/3) = sin(pi/2 + 4pi/3) = -0.5
#3 cos(4pi/3) = -cos(pi + 4pi/3) = -0.5
#4 cos(4pi/3) = -cos(pi - 4pi/3) = -0.5
See, as shown, they all work.
I have seen the triangles and know how they are derived, but my main question is, if I am given a question that asks for the equivalent trig ratio in terms of its cofunction identity, is there a specific one I should use when I am doing these types of question?
Your help is much appreciated.