Download Pre-Calculus 4 - Brown Deer Middle/High School

Pre-Calculus 4.3
Trigonometric functions
or…Soak your toes in what, now?
Welcome to trigonometric function review!
Define:
sin θ =
θ
cos θ =
tan θ =
sec θ =
=
csc θ =
=
cot θ =
=
Trigonometric Functions of Special Right Triangles
Fill in the missing leg and hypotenuse.
45˚
In a 45-45-90:
Hypotenuse =
Find:
sin 45˚ =
sec 45˚ =
45˚
1
cos 45˚ =
csc 45˚ =
tan 45˚ =
cot 45˚ =
Fill in the missing leg and the hypotenuse
In a 30-60-90:
60˚
Hypotenuse =
1
Long leg =
Find:
sin 30˚ =
sec 30˚ =
cos 30˚ =
csc 30˚ =
tan 30˚ =
cot 30˚ =
sin 60˚ =
sec 60˚ =
cos 60˚ =
csc 60˚ =
tan 60˚ =
cot 60˚ =
30˚
Trigonometric Identities
Cofunction Identities
Look at the values of sin 60˚ and cos 30˚. What do you notice?
How about sec 30˚ and csc 60˚?
This is true for all complementary angles, or to put it another way:
sin( 90   )  cos 
cos(90   )  sin 
tan( 90   )  cot 
cot(90   )  tan 
sec( 90   )  csc 
csc( 90   )  sec 
or: Cofunctions of complementary angles are equal.
Reciprocal Identities
1
1
sin  
cos  
csc 
sec 
csc  
1
sin 
Quotient Identities
sin 
tan  
cos 
sec  
1
cos 
cot  
tan  
1
cot 
cot  
1
tan 
cos 
sin 
Pythagorean Identities
sin 2   cos 2   1
1  tan 2   sec 2 
1  cot 2   csc 2 
Use the trigonometric identities to find the following:
1) sin  0.6 Find the values of cos  and tan  .
2) Find sin , cos  , cot  , csc  , and sec  if you know that
tan  = 3.
3) A surveyor stands 50 feet away from a tree. The angle of
elevation to the top of the tree is 71.5˚. What is the height of the
tree?
4) A twelve meter flagpole casts a 9-meter shadow. Find the
angle of elevation to the sun.
Assignment:p.387#1-21odds,33-37odds,43,44,47,49,63-69odds