1. Warm Up The terminal side passes through (1, -2), find cosƟ and sinƟ.
The sine of an angle is − 𝟓 𝟏𝟑 . The angle is in Quadrant IV. What is the cosine of the angle?
Find the reference angles for 𝟑𝟖𝝅 𝟐𝟏 and − 𝟏𝟖𝝅 𝟏𝟑
Solve in radians: cosƟ = 0
Find the exact value of 𝒍𝒐𝒈 𝟒 𝒔𝒊𝒏𝟏𝟓𝟎°
− 𝟐 𝟓 𝟓 𝟓 𝟓
𝟏𝟐 𝟏𝟑
𝟒𝝅 𝟐𝟏 , 𝟓𝝅 𝟏𝟑
𝝅 𝟐 ±𝒏𝝅
− 𝟏 𝟐

2. Graphing Sine and Cosine Functions
Complete classwork problems A – D
You should have a table, 2 complete graphs (on the same grid), and key points in degrees and radians for each graph.

3. Use the unit circle to complete the table for each function.
Graph y=sin x.
Use a scale of 𝜋 12 radians on the x-axis and 0.1 on the y-axis.
D. For each graph, find the following in radians and degrees: period zeroes y-intercept amplitude domain range x
𝜋 6
𝜋 4
𝜋 3
𝜋 2
2𝜋 3
3𝜋 4
5𝜋 6 𝜋
7𝜋 6
5𝜋 4
4𝜋 3
3𝜋 2
5𝜋 3
7𝜋 4
11𝜋 6 2𝜋
y=sin x
y=cosx

4. Graph Sine & Cosine
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1 𝟐𝝅
-0.1
𝝅 𝟏𝟐 𝝅
-0.2
-0.3
-0.4
-0.5
-0.6
-0.7
-0.8
-0.9
-1.0

5. 𝒚=𝒔𝒊𝒏𝒙 Period: 2𝜋, 360 Amplitude: 1 Domain: −∞<𝑥<∞ Range: −1≤𝑦≤1
1.0
Period: 2𝜋, 360
Amplitude: 1
Domain: −∞<𝑥<∞
Range: −1≤𝑦≤1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
𝝅 𝟏𝟐
𝝅 𝟔
𝝅 𝟒
𝝅 𝟑
𝟓𝝅 𝟏𝟐
-0.1
𝝅 𝟐
𝟕𝝅 𝟏𝟐
𝟐𝝅 𝟑
𝟑𝝅 𝟒
𝟓𝝅 𝟔
𝟏𝟏𝝅 𝟏𝟐 𝝅
𝟏𝟑𝝅 𝟏𝟐
𝟕𝝅 𝟔
𝟓𝝅 𝟒
𝟒𝝅 𝟑
𝟏𝟕𝝅 𝟏𝟐
𝟑𝝅 𝟐
𝟏𝟗𝝅 𝟏𝟐
𝟓𝝅 𝟑
𝟕𝝅 𝟒
𝟏𝟏𝝅 𝟔
𝟐𝟑𝝅 𝟏𝟐 𝟐𝝅
-0.2
-0.3
-0.4
-0.5
Zeroes: 0,𝜋,2𝜋
0ᵒ,180ᵒ,360 ̊
y-intercept: (0,0)
-0.6
-0.7
-0.8
-0.9
-1.0

6. 𝒚=𝒄𝒐𝒔𝒙 Zeroes: 𝜋 2 , 3𝜋 2 90ᵒ, 270 ̊ y-intercept: (0,1)
1.0
0.9
0.8
Zeroes: 𝜋 2 , 3𝜋 2
90ᵒ, 270 ̊
y-intercept: (0,1)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
𝝅 𝟏𝟐
𝝅 𝟔
𝝅 𝟒
𝝅 𝟑
𝟓𝝅 𝟏𝟐
-0.1
𝝅 𝟐
𝟕𝝅 𝟏𝟐
𝟐𝝅 𝟑
𝟑𝝅 𝟒
𝟓𝝅 𝟔
𝟏𝟏𝝅 𝟏𝟐 𝝅
𝟏𝟑𝝅 𝟏𝟐
𝟕𝝅 𝟔
𝟓𝝅 𝟒
𝟒𝝅 𝟑
𝟏𝟕𝝅 𝟏𝟐
𝟑𝝅 𝟐
𝟏𝟗𝝅 𝟏𝟐
𝟓𝝅 𝟑
𝟕𝝅 𝟒
𝟏𝟏𝝅 𝟔
𝟐𝟑𝝅 𝟏𝟐 𝟐𝝅
-0.2
-0.3
Period: 2𝜋, 360 ̊
Amplitude: 1
Domain: −∞<𝑥<∞
Range: −1≤𝑦≤1
-0.4
-0.5
-0.6
-0.7
-0.8
-0.9
-1.0

7. Section 7-5 The Other Trigonometric Functions
Objective: To find the values of the tangent, cotangent, secant, and cosecant functions
and to sketch the functions’ graphs.

8. We can define other trig functions in terms of (x,y) and r.
𝑐𝑜𝑠𝜃= 𝑥 𝑟
𝑠𝑖𝑛𝜃= 𝑦 𝑟
We can define other trig functions in terms of (x,y) and r.
Name
Abbreviation
Definition
tangent of 
tan 
cotangent of 
cot 
secant of 
sec 
cosecant of 
csc 

9. What is sin ÷ cos? tan What is cos ÷ sin? cot 𝑦 𝑟 ÷ 𝑥 𝑟 = 𝑦 𝑟 ∗ 𝑟 𝑥 =
𝑦 𝑥 =
tan
What is cos ÷ sin?
𝑥 𝑟 ÷ 𝑦 𝑟 =
𝑥 𝑟 ∗ 𝑟 𝑦 =
𝑥 𝑦 =
cot

10. Reciprocals tan & cot are reciprocals cos & sec are reciprocals
sin & csc are reciprocals

11. Find the value of each expression to four significant digits.
A.) tan 203°
B.) cot 165°
C.) csc (-1)
D.) sec 11
Hint:

12. Find the value of each expression to four significant digits.

13. Graph 𝑦= tan 𝜃 −3𝜋≤𝜃≤3𝜋 Window xmin: −3𝜋 xmax: Table Setup xscl:
ymin:
ymax:
yscl:
xres:
−3𝜋
Table Setup
TblStart: 0
∆Tbl: 𝜋 4
Indpnt: Auto
Depend: Auto: 3𝜋
𝜋 4
−10 10 1 1

14. Graph 𝑦= tan 𝜃 −3𝜋≤𝜃≤3𝜋
Domain
Range
Period
Asymptotes

15. Graph 𝑦= sec 𝜃 −3𝜋≤𝜃≤3𝜋
Domain
Range
Period
Asymptotes

16. Graph 𝑦= sec 𝜃 −3𝜋≤𝜃≤3𝜋
Why can’t 𝑠𝑒𝑐𝜃 be between
-1 and 1?

18. Homework
Finish All Graphs