Transcript Here
WARM UP
1. Determine two coterminal angles (in
degrees) for 114°
2. Find (if possible) the complement and
supplement of 36°
3. Convert 315° to radians
4. Convert 7π/3 to degrees
5. Convert 310.75° to D°M'S"
4.2
The Unit Circle
Here It Is…
There are 6 Trigonometric
Functions
Let t be a real number and (x, y) be the point on the
unit circle corresponding to t.
• sin t = y
• csc t = 1/sin t = 1/y
• cos t = x
• sec t = 1/cos t = 1/x
• tan t = y/x
• cot t = 1/ tan t = x/y
Examples
Evaluate the six trig functions for each:
1. t = π/6
2. t = 5π/4
1)
Answers
3 1
correspond s to , so
6
2 2
1
1
csc 2
sin y
2
6 y
6
3
cos x
6
2
y
3
tan
6 x
3
1 2 2 3
sec
3
3
6 x
x
3
cot
6 y
5
2
2
so
2)
correspond s to
,
4
2
2
5
2
5 1
sin
y
csc
2
4
2
4
y
5
2
cos
x
4
2
5 y
tan
1
4
x
5 1
sec
2
4 x
5 x
cot
1
4
y
Evaluate sin 13π/6 using its period
as an aid.
Because 13π /6 = 2π + π/6 it follows that…
sin 13π/6 is the same as π/6 which is equal to ½.
Therefore sin 13π/6 = ½
Even and Odd Trig Functions
The cosine and secant functions are even.
cos (-t) = cos t
sec (-t) = sec t
The sine, cosecant, tanget and cotangent are odd
sin (-t) = - sin t
tan (-t) = - tan t
csc (-t) = - csc t
cot (-t) = - cot t
**This is true because of the rules from chapter
1 that say if f(-x) = f(x) then it is even.
And if f(-x) = -f(x), then it is odd.