Download Section 5.2 Trigonometric Functions of Real Numbers

Section 5.2
Trigonometric Functions of Real
Numbers
Objectives:
•Compute trig functions given the
terminal point of a real number.
•State and apply the reciprocal and
Pythagorean identities of trig
functions.
Class Work
Fill out the unit circle.
Definition of the Trigonometric Functions
Let t be any real number and let P(x,y) be the
terminal point on the unit circle determined
by t. We define
sin t  y
1
csc t  ( y  0)
y
y
cos t  x
tan t 
x
1
x
sec t  ( x  0) cot t   y  0 
x
y
Ex 1. Find the six trig functions of each given
real number t.

a) t 
6

b) t 
2
Signs of Trig Functions
Quadrant
I
II
III
IV
Positive
Ex 2 Determine the sign of the following trig
functions.
a) cos

3
b) tan 4
7
c) sin
4
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 3 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
Ex 4. Use your calculator to find an approximate
value of the trig function at t. (Your calculator must
be in radian mode!!)
a) sin 2.2
b) cos 4.1
c) cot 28
d) csc0.98
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
Use your calculator to find an approximate
value.
9. sin 0.52
10. cos3.2
11. cot1.7
12. sec12
Fundamental Identites
3
cos t 
5
Ex 5. If
and t is in quadrant IV, find the
values of all the trig functions at t.
Ex 6. Write tan t in terms of cos t, where t is in
quadrant III.
Ex 7. Write cos t in terms of sin t, where t is in
quadrant IV.
Ex 8 Write csc t in terms of cot t, where t is in
quadrant III.
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. csc t  2 sint < 0
Write the first expression in terms of the second
if the terminal point is in the given quadrant.
16. tan t, cos t quad III
17. sin t, sec t quad IV
HW #2 p416 3-19 eoo, 23-26 all,
27-35eoo, 63-69 odd