4.2 Notes – Unit Circle
Objectives: You should
1.
2.
3.
4.
be able to draw and correctly label the unit circle.
be able to use the coordinates of the points on the unit circle to find trig values at a given point.
know the domain and period of sine and cosine.
be able to use a calculator to evaluate trig expressions.
Vocabulary: unit circle, sine, cosine, tangent, cotangent, secant, cosecant, domain, period, periodic
Unit circle: the circle given by the equation x2 + y2 = 1
Where is the center of the circle? _____________
What is the largest x-value? __________ smallest? __________
What is the largest y-value? __________ smallest? __________
Unit circle activity (separate page)
Definitions of Trigonometric Functions: Let  be a real number (specifically an angle measure) and let (x, y)
be the point on the unit circle that corresponds to .
sin 𝜃 = 𝑦
tan 𝜃 =
𝑦
,𝑥 ≠ 0
𝑥
sec 𝜃 =
1
,𝑥 ≠ 0
𝑥
cos 𝜃 = 𝑥
cot 𝜃 =
𝑥
,𝑦 ≠ 0
𝑦
csc 𝜃 =
1
,𝑦 ≠ 0
𝑦
Unit circle table (separate page)
Use a calculator to evaluate the trig functions.
1. sin
11𝜋
9
2. cos 58°
3. csc −13.4
Assignment: pg. 270 #13-29 eoo, 53-69 odds
Angle Measure
degrees
radians
0
𝜋
6
45
60
90
2𝜋
3
135
150
180
𝜋
210
5𝜋
4
240
3𝜋
2
300
315
330
360
sin
cos
Trig Function Values
tan
cot
sec
csc