I can graph cosine and complete
the unit circle
Warm Up
Solve for x:
1. 𝒔𝒊𝒏 𝟏𝟓° = 𝟑𝒙
2.
30
22°
3.
1
𝑥
𝑥
4. Rationalize the denominator
𝟐
𝟑
𝟏
a.
b.
c.
𝟖
2
𝟔
𝟒 𝟐
d.
𝟖
𝟑 𝟔
Warm Up
Solve for x:
1. 𝒔𝒊𝒏 𝟏𝟓° = 𝟑𝒙
Solve for x:
2.
22°
𝑥
Warm Up
30
3.
2
1
𝑥
Warm Up
Solve for x:
4. Rationalize the denominator
𝟐
𝟑
a.
b.
c.
𝟖
𝟔
𝟏
𝟖
𝟒 𝟐
d.
𝟑 𝟔
Homework Questions
Graphing Cosine
• Create a table similar to the one we used to find
the height of a rider on The Screamer
• Using the 8.1.4 Resource Page as a reference,
find the horizontal distance for each angle given
15°
𝑥
• When you have table values, create a graph
How does this graph compare to the graph of sine?
2 minute stretch break
Thinking
about a
rider’s
distance
from the
ground, what
do you
notice
looking at
the graph?
Degree
Height
Degree
Height
0
15
30
45
60
75
90
105
120
135
150
165
180
0
25.88
50
70.71
86.60
95.59
100
95.59
86.60
70.71
50
25.88
0
195
210
225
240
255
270
285
300
315
330
345
360
-25.88
-50
-70.71
-86.60
-95.59
-100
-95.59
-86.60
-70.7
-50
-25.88
0
Thinking
about a
rider’s
distance
from the
ground, what
do you
notice?
Degree
Height
Degree
Height
0
15
30
45
60
75
90
105
120
135
150
165
180
0
25.88
50
70.71
86.60
95.59
100
95.59
86.60
70.71
50
25.88
0
195
210
225
240
255
270
285
300
315
330
345
360
-25.88
-50
-70.71
-86.60
-95.59
-100
-95.59
-86.60
-70.7
-50
-25.88
0
Looking at
the angles
where riders
are the same
distance
from the
ground, what
do you
notice?
180 −165°
𝜃°
15°
𝜃°
195°
180 + 𝜃°
245°360 − 𝜃°
BREAK!
Unit Circle
Solve for 𝑦
sin 30 = 𝑦
1
𝑦=
2
Solve for 𝑥
60°
𝑦
30°
𝑥
cos 30 = 𝑥
𝑥 = .86660
Is there another way to
solve?
Unit Circle
Solve for 𝑥
60°
2
1
+ 𝑥 2 = 12
2
1
+ 𝑥2 = 1
4
3
2
𝑥 =
4
𝑦
𝑥=
30°
𝑥
3
4
3
𝑥=
2
What we know so far…
Homework
Textbook:
8-15, 8-17, 8-26, 8-27
Unit Circle
Solve for 𝑥
cos 45 = 𝑥
𝑥 = .70710678
45°
𝑦
45°
𝑥
Unit Circle
Solve for 𝑥
45°
𝑥
Is there another way to solve for 𝑥?
𝑥 2 + 𝑦 2 = 12
𝑥2 + 𝑥2 = 1
2𝑥 2 = 1
1
2
45°
𝑥 =
2
𝑥𝑦
1
𝑥=
2
2
𝑥=
2
Unit Circle
Solve for 𝑥 and 𝑦
1
𝑥=
2
3
𝑦=
2
30°
𝑦
60°
𝑥
Unit Circle
Using what we have discussed about patterns,
try to fill in the rest of the unit circle