Download 4) CSC X

Precalculus
Name
Mr. Carell
Date
S.1-5.2 Quiz Review
Period
Simplifying and Verifying Trig Identities Strate~
1) Begin with the more complicated side of the identity and work toward
making it look like the simpler side.
2) Use algebraic manipulations such as multiplying, factoring, finding common
denominators and combining fractions,
3) Use Reciprocal and Pythagorean Identities to simplify whenever possible.
4) Rewrite expressions in terms of sine and cosine.
Simplify each trigonometric expression.
1) sin2x + cos2x + tan2x
cosx sinx cos2x
2)--+--+~
secx cscx sm x
3] sinx(tanx + cotx)
4) CSC X ~ COS X cot X
5) tan~x+l cotx +1
tan~ x tanx
6) sec2x-c°sax
tan2 x
Veri _fy each trigonometric identity.
cot x csc x + sec x = csca x sec x
7) tan~x cosZx = 1 - cos2x
9) secx
--+---cscx secx + cscx
tanx cotx
ll) c°t2x =cscx-1
1 + csc x
sinx
10}- sinx +
= 2cscx
l-cosx l+cosx
COSX
12)l+sinx-~
= 2secx
cos x 1 + sin x
NAME
DATE
PERIOD_
Verifying Trigonometric identities
Verify Trigonometric identities To verify an identity means to
pi’ove that both sides of the equation are equal for all values of the variable
for which both sides are defined.
Verify that sec2 x -- 1 = sill2 X.
The left-hand side of this identity is more complicated, so start with that
expression first.
sec2x- 1
sec2 x
(tan2x+ i)-- 1
sec2 x
Pythagorean ~dentity
sec2 x
Simplify,
Quotient Identity and Reciprocal Identity
sin2 x . cos2 x
0082 X
= sin2x q/
Simplify.
Multiply.
Notice that the verification ends with the expression on the Other side of the
identity.
Verify each identity.
1. sec O- cos 0 = sin Otan 0
2. sec 0 = sin O(tan 0 + cot 0)
3, tan tO Csc 0 cos tO = 1
20 =sec~0
4. csc20-c°t
1 - sin20
Chapter 5
10
Glencoe Precalculus