Download Algebra II Honors

Algebra II Honors
9.7: Using Trigonometric Identities (PC 5.1, 5.2)
HW: p.517 (12-20 even, 24-30 even)
Trig Identities
• Pythagorean Identities
sin u  cos u  1
2
2
1  tan 2 u  sec 2 u
1  cot u  csc u
2
2
• Even/Odd Identities
sin( u )   sin u csc( u )   csc u
cos( u )  cos u sec( u )  sec u
tan( u )   tan u cot( u )   cot u
Trig Identities
• Cofunction Identities


sin   u   cos u
2



tan   u   cot u
2



sec  u   csc u
2



cos  u   sin u
2



cot   u   tan u
2



csc  u   sec u
2

Simplify the Trig Expression
1.) sin x cos x  sin x
2
Simplify the Trig Expression
PC: P.381 (#22)
2.) (1  sin x)(sec x)
2
Check using your calculator:
Y1= Question
Y2= Answer
Check: graphs/tables are
the same
Simplify the Trig Expression
PC: P.381 (#30)


cos   x 
2


3.)
cos x
2
Verify the Identity Algebraically.
PC: P.381 (#46)
4.) cos sec   cos   sin 
2
2
PC: P.381 (#66)
Verify.
csc x  1
5.)
 csc x  1
csc x  1
2
Verifying Trig Identities
1.) Work with one side.
2.) Look for opportunities to factor an
expression, add fractions, square a binomial,
or create a monomial denominator.
3.) Look for opportunities to use the
fundamental identities.
4.) If the preceding guidelines do not help, try
converting to all sines and cosines.
5.) Try something! Even making an attempt
that leads to a dead end gives insight.
Verify the Identity Algebraically.
PC: P.381 (#56)
1  csc 
6.)
 sec 
cot   cos 
Multiply and simplify.
PC: P.381 (#72)
7.) cot x  csc xcot x  csc x
Verify.
PC: P.381 (#76)
1
1
2
8.)

 2 cot x
sec x  1 sec x  1

Verify the Identity.


9.) tan x  1 cos x  1   tan x
2
2
2
Verify the Identity.
cos x
10.) sec x  tan x 
1  sin x
Verify the Identity.
sec   1
2
11.)
 sin 
2
sec 
12.) tan x  cot x  sec x csc x
2
cot 
1  sin 
13.)

1  csc 
sin 
2
1
1
2
14.)

 2 sec 
1  sin  1  sin 
Verify the Identity.
2
cot 
1  sin 
13.)

1  csc 
sin 