College Algebra/Trig Summer Workshop
Simplifying Trigonometric Expressions
√
Simplify the expression
Name:
9 − x2
by making the substitution x = 3 sin θ
x2
Algebraically simplify the expression
the expression.
Use trig identities to re-write
√
x2 − 4x + 13 and then make a trig substitution to further simplify
sin3 x
as a product.
cos x
Class Examples
a) Simplify the expression √
b) Simplify the expression
x
by making the substitution x = 2 tan θ
x2
+4
√
1
by making the substitution x = 2 sec θ
x2 − 4
x2
c) Use trig identities to re-write
cos θ
as a product.
sin2 θ
d) Use trig identities to simplify (sin x + cos x)2 as much as possible.
e) Algebraically simplify the expression
the expression.
√
x2 + 4x + 5 and then make a trig substitution to further simplify
Homework Problems
1) Simplify the expression √
√
2) Simplify the expression
1
by making the substitution x = 4 tan θ
+ 16
x2
x2 − 9
by making the substitution x = 3 sec θ
x3
3) Use trig identities to re-write
tan θ
as a product.
sec2 θ
q
2
4) Use trig identities to simplify (1 + sin θ) + cos2 θ as much as possible.
5) Algebraically simplify the expression √
x2
1
and then make a trig substitution to further
− 6x + 13
simplify the expression.
6) For a certain problem, you use the substitution x = 3 sec θ and get 2 sin (2θ) + C for your answer.
Express this answer in terms of x by re-substituting for θ.