Verifying Trigonometric Identities

advertisement
Pre calculus Problem of the Day
Homework p. 578 1-21 odds
Simplify the following:
  2   2
a) sin   cos 
 6   6 
  2   2
b) sin   cos 
 4   4 
 4  2  4  2
c) sin   cos 
 3  
3 
Trigonometric Identities - a statement of equality that is
true for all values where the function is defined.
Reciprocal Identities:

1
sin 
csc 
1
cos 
sec 
1
tan  
cot 
1
csc  
sin 
1
sec  
cos
1
cot  
tan 
Quotient Identities:

sin
tan  
cos
cos
cot  
sin
Pythagorean Identities:
Even/Odd Identities:
sin 2   cos2   1
sin   sin
1 cot 2   csc 2 
cos   cos
tan  1  sec 
2
2



tan   tan
Verifying Trigonometric Identities
To verify a trigonometric identity we must show that one side of
the identity can be simplified so that it is identical to the other
side or each side can be simplified independently until they are
identical.
Never treat an identity like an equation. We are not solving
for the variable.
Techniques for verifying trigonometric identities.
1) Rename using the fundamental identities.
2) Rewrite a more complicated side in terms of sines and
cosines.
3) Factor.
4) Combine fractional expressions using an LCD.
5) Separate a single-term quotient into two terms.
6) Multiply the numerator and denominator on one side by a
binomial factor that appears on the other side of the
identity.
Maeve
Miranda
Ryan
Laurel
Brent
Peyton
John
Jessica
Bianca
Carson
Sarah
Weilun
Chelsea R.
Matt
Katie
Kevin
Chelsea K.
Lindsay
Lindsey
Rachel
Jules
Lisa
Jenn Casey Leah
Brian
Hayley
Kelsey
Danielle
Rebecca
Miles
Blake
Eleanor
Jenn Co
Olivia
Carola
Download