Download Pre-Calculus Section 5

Pre-Calculus Section 5.2
Objective: SWBAT understand trigonometric functions as a circular function.
Homework: Day 1 Page 416 # 1 – 25 odd and Section 5.2 Worksheet
Day 2 Page 416 # 27 – 69 odd (skip 37 – 43 odd)
Daily Warm – Up
If tan  
2
and  is in quadrant III, find the other 5 trig values.
3
1. Let t be any real number and let P(x, y) be the terminal point on the unit circle
determined by t. We define the trig functions as follows:
sin t  y
csc t 
1
y
cos t  x
 y  0
sec t 
1
x
 x  0
tan t 
y
x
 x  0
cot t 
x
y
 y  0
2. Since all the trig functions can be defined using the unit circle, they are often referred
to as circular functions.
3. Find the six trig functions.
Angle
 0
  30
  45
  60
  90
P  0,1
t value
Terminal
Point
sin 
cos 
tan 
csc 
sec 
cot 
4. Determine the sign of the trig functions for angles located in all four quadrants.
5. Determine the six trig functions for each angle.
Trig
Function
sin 
cos 
tan 
csc 
sec 
cot 
t

3
t
19
4
t
3
4
t
17
6
t
7
3
6. Reciprocal Identities
csc t 
1
sin t
sec t 
1
cos t
tan t 
sin t
cos t
cot t 
cos t
sin t
cot t 
1
tan t
7. Odd and Even trig functions.
cost
cos  t   cos t
Even function
sin  t    sin t
Odd function
sect
sin t
csct
tan t
cot t
8. The Pythagorean Identities
Proof
a.
sin 2 t  cos 2 t  1
b.
tan 2 t  1  sec 2 t
c.
1  cot 2 t  csc 2 t
9. Revisit right triangle trig
sin t 
opposite
hypotenuse
cos t 
adjacent
hypotenuse
tan t 
opposite
adjacent
cot t 
adjacent
hypotenuse
csc t 
hypotenuse
opposite
sec t 
hypotenuse
adjacent
3
10. If cos t  and t is in quadrant IV, find the values of all six trig functions at t.
5
11. Write tan t in terms of cost , where t is in quadrant III.
Section 5.2 Worksheet

6
0

4

3
2
3

2
3
4

5
6
sin 
cos
tan 
csc
sec
cot 
7
6
sin 
cos
tan 
csc
sec
cot 
5
4
4
3
3
2
5
3
7
4
11
6
2
25
2