Unit Circle
I. Give the exact answers for the coordinates of the points below using special right triangle ratios.
Use the unit circle to give exact answers for the following; no double denominators; rationalize, too!
sin 0 = ______
cos 0 = ______
tan 0 = ______
sin 30 = ______
cos 30 = ______
tan 30 = ______
sin 45 = ______
cos 45 = ______
tan 45 = ______
sin 60= ______
cos 60 = ______
tan 60 = ______
sin 90 = ______
cos 90 = ______
tan 90 = ______
Unit Circle
II. Determine the measure of each angle. Then, find the exact value of the sine, cosine, and tangent for each
angle. Rationalize all denominators; do not use double denominators.
B (4, 4 3)
A
C
(a)
m  BAC = ______
(a)
m  BAC = ______
(a)
m  BAC = ______
(b)
sin ______ = ______
(b)
sin ______ = ______
(b)
sin ______ = ______
(c)
cos ______ = ______
(c)
cos ______ = ______
(c)
cos ______ = ______
(d)
tan ______ = ______
(d)
tan ______ = ______
(d)
tan ______ = ______
(e)
m  ABC = ______
(e)
m  ABC = ______
(e)
m  ABC = ______
(f)
sin ______ = ______
(f)
sin ______ = ______
(f)
sin ______ = ______
(g)
cos ______ = ______
(g)
cos ______ = ______
(g)
cos ______ = ______
(h)
tan ______ = ______
(h)
tan ______ = ______
(h)
tan ______ = ______
(l)
AB =
(l)
AB =
(l)
AB =
________
________
________
(a)
m  BAC =
____
(a)
m  BAC =
____
(a)
m  BAC =
____
(b)
sin ____=
____
(b)
sin ____=
____
(b)
sin ____=
____
(c)
cos ____=
____
(c)
cos ____=
____
(c)
cos ____=
____
(d)
tan ____=
____
(d)
tan ____=
____
(d)
tan ____=
____
Unit Circle
3. Refer to the following diagrams:
(a) Find the coordinates of A, C, and D.
(b) Find the slope of AO .
(c) Find the tangent of 45 degrees.
(d) Find the slope of CO .
(e) Find the tangent of 30 degrees.
(f) Find the slope of DO .
(g) Find the tangent of 60 degrees.
(h) Describe the slope in terms of a trigonometric ratio.
Unit Circle
4. Use the unit circles below or the unit circle on the first page to determine the following. Give the exact
answers for the coordinates of the points below using special right triangle ratios.
sin 30º
=
_______
cos 30º
=
_______
tan 30º
=
_______
sin 45º
=
_______
cos 45º
=
_______
tan 45º
=
_______
sin 60º
=
_______
cos 60º
=
_______
tan 60º
=
_______
sin 90º
=
_______
cos 90º
=
_______
tan 90º
=
_______
sin 120º =
_______
cos 120º =
_______
tan 120º =
_______
sin 135º =
_______
cos 135º =
_______
tan 135º =
_______
sin 150º =
_______
cos 150º =
_______
tan 150º =
_______
sin 180º =
_______
cos 180º =
_______
tan 180º =
_______
sin 210º =
_______
cos 210º =
_______
tan 210º =
_______
sin 225º =
_______
cos 225º =
_______
tan 225º =
_______
sin 240º =
_______
cos 240º =
_______
tan 240º =
_______
sin 270º =
_______
cos 270º =
_______
tan 270º =
_______
sin 300º =
_______
cos 300º =
_______
tan 300º =
_______
sin 315º =
_______
cos 315º =
_______
tan 315º =
_______
sin 330º =
_______
cos 330º =
_______
tan 330º =
_______
sin 360º =
_______
cos 360º =
_______
tan 360º =
_______