Download Trig #4 Exact Values

Pre-Calc Book Section 5.2
Trigonometric Functions
of Real Numbers
Objectives:
• How do you find the value of any given trig
angle?
• How can understanding the signs of the
quadrants help in finding the function value of
any trig angle?
Trigonometric Functions
of Any Angle
y
sin  
r
x
cos  
r
y
tan   , x  0
x
r
csc   , y  0
y
r
sec   , x  0
x
x
cot   , y  0
y
Ex. 1 Find the six trig functions of each given
real number t.

a) t  6

b) t 
2
 1 3
 ,

2
2


Ex.2 Let
be a point on the terminal side
of . Find the sine, cosine, and tangent of .
Ex.3 Let (-3,4) be a point on the terminal side
of . Find the sine, cosine, and tangent of .
Signs of Trig Functions
 ,  
 , 
 ,  
 , 
Quad
I
II
III
IV
Positive
All Trig. Functions
Sine/Cosecant
Tangent/Cotangent
Cosine/Secant
All Students Take Calculus
Ex. 4 Determine the sign of the following trig
functions.
a) cos 

> 0, because the terminal point of t 
is in Quad I
3
3
b) tan 4
c)
> 0, because the terminal point of t  4 is in Quad III
7
7
< 0, because the terminal point of t 
sin
4
4
is in Quad IV
Class Work
Find the six trig functions of each given real
number t.

1. t 
4

2. t 
3
Determine the sign of the following trig
functions.
3.
5
tan
6
4. cos

7
5. csc 5
4
Ex 5. Evaluate the sine, cosine and tangent
of the given angle.
a ) 570
b)  60
13
c)
4
11
d)
3
Ex. 6 Find the exact value of the trig function at
the given real number t.
2
a) cos
3
 
b) tan   
 3
c)
19
sin
4
d)
 2 
cos  

3


e)
 5 
sin   
 3 
f)
 5 
tan   
 6 
Class Work
Find the exact value of the trig function at the
given real number t.
6.
5
sin
6
7.
 4 
tan  

3


8.
14
cos
3
Ex.7 State the quadrant in which  lies.
a) cos   0, sin   0
b) sec   0, tan   0
c) sin   0, cot   0
Fundamental Identites
Ex 8. If
3
cos t 
5
and t is in quadrant IV, find the
values of all the trig functions at t.
Ex 9. Find the values of the six trig functions of
 in the given quadrant.
5
a) tan   
4
cos   0
b) csc   3 tan   0
2
c) sin   
7
cot   0
Class Work
Find the values of all the trig functions of t from
the given information.
13.
4
cos t  
5
14.
1
tan t 
4
In quad III
In quad III
15. sec t  2 sint < 0
HW #3 p.416 3-19 eoo,
27-35 eoo, 63-69 odd