Homework Questions
Section 3.1­­Reference Angles
The reference angle of any angle in standard position is the acute angle between its terminal side and the x­axis. θ = 95o
θ = 340o
Original Angle
150o
210o
330o
­51o
­135o
370o
185o
θ = 200o
θ = 55o
Reference Angle
θ = 355o
θ = ­15o
Why do we care about reference angles?
Use your calculator to find each of the following:
sin 30o
sin 150o
sin 210o
sin 330o
What conclusion can we make?
You are supposed to have some values memorized...
sin 30o
cos 30o
sin 45o
cos 45o
sin 60o
cos 60o
They come up so often that you should know them!
How will we use reference angles?
To calculate the value of sinθ, cosθ, tanθ, cscθ, secθ, or cotθ...
(1) Note the quadrant of the original angle θ
and the SIGN of the trig function there!
(2) Calculate the value of the reference angle
(3) Find the trig function value using the reference angle, then adjust the sign.
EXAMPLES:
Find the EXACT value of cos 135o
Find the exact value of sin 240o.
Find the exact value of tan 150o.
Find the exact value of sec 300o.
NOW we can use the reference angle to help us find solutions to trig equations.
Find θ if sinθ =
Find θ if cosθ = ­0.9455
Find θ if tanθ = 0.0349
θ is in QIV and 0o < θ < 360o
θ is in QIII and 0o < θ < 360o
θ is in QIII and 0o < θ < 360o
Find θ if cscθ = 3.8637
θ is in QII and 0o < θ < 360o