MATH 11022:
Half Angle Identities
sin
x
cos
tan
tan
tan
2
x
2
x
2
x
2
x
2
r
=±
r
=±
1 − cos x
2
1 + cos x
2
r
1 − cos x
=±
1 + cos x
=
sin x
1 + cos x
=
1 − cos x
sin x
NOTE: The ± sign is determined by the quadrant in which the angle
Example 1: Find the exact value of
(a)
sin 22.5◦ =
x
terminates.
2
2
MATH 11022: HALF ANGLE IDENTITIES
(b)
cos 157.5◦ =
(c)
cot β2 , given tan β = −
√
5
2
with 90◦ < β < 180◦ .