Download Angles and the Unit Circle

Warm Up
1. Given the following trig
value, sketch a
triangle and find the
remaining 5 ratios.
Mar.
st
31
2. Use Pythagorean theorem
to solve for x then find
all six trig ratios for θ.
csc   3
3. Convert 150○ to radians.
4. Convert 5π/4 to degrees.
Homework Check & Questions?
• 1.
Quick Review or Right Triangle
Trig & Angle Measures
Building & Using The Unit Circle
Examples
• Let (6, 8) be a point on the terminal side of . Find all
six trig ratios.
Examples (cont.)
• Let (-5, -12) be a point on the terminal side of . Find
all six trig ratios.
Examples (cont.)
• Find the values of the 6 trig functions of .
2
tan    and  lies in quadrant IV
5
What quadrant are you in if…
cos   0 and csc   0
sin   0 and tan   0
sec   0 and cot   0
• Standard Position
• Positive and Negative Angles
• Wrapping Angles
Degrees, Minutes, Seconds…
1) Change 25.36○ to degrees, minutes,
seconds.
2) Change -175○ 30’ 45” to decimal
degrees.
Angles…
Determine the quadrant in which the
terminal side of the angle lies and
sketch the angle in standard position.
1) 100○
2) -290○50’
3) 9π/5
4) -2.5
Coterminal Angles…
• Determine two coterminal angles (one
negative and one positive) for each given
angle.
1) 140○
2) 3π/7
Use Geometry to determine the exact value of the
missing side length of each special right triangle.
Complete the first quadrant of the Unit Circle
A reference angle is the acute angle formed by
the terminal side of an angle in standard position
and the x-axis.
What is the reference angle for …
310º
-210º
3π/4
11π/7
Complete the angles (in radians & degrees) the Unit Circle
The Unit Circle
Using the Unit Circle
Find the point on the unit circle that corresponds
to the angle.
1) -120○
2) 495○
3) -30 ○
5
4)
6
13
5)
3
3
6) 
2
Practice
Evaluate each of the following.
7)cos (150 ○)
 17 

10) sin 
 6 
8) sin (360 ○)
 2 
11) sin   3 


11
9) cos
6
5
12) sin
4
Trig Functions
(and their relationship to sine/cosine)
tan  
cot  
sec  
csc  
sin 
cos 
cos 
1
or
sin 
tan 
1
 (flip over the cos)
cos 
1
 (flip over the sin)
sin 
More Practice
Evaluate each of the following.
1. tan(240○)
2. csc(-225○)
3) cot(20π/3)
4) sec(- π/4)
Examples (cont.)
• Let (-4, 0) be a point on the
terminal side of . Find all six
trig ratios.
• Let (0, 9) be a point on the
terminal side of . Find all six
trig ratios.
Extra Practice
Find all 6 trig ratios from the given information.
1.
2. sinθ = 8/13

4. (6, -6)

18
14
3. cotθ = 5
5. (-1, -2)
6. cosθ = -1/2, where θ lies in Quadrant II
More Extra Practice
• No calculator…
1. Determine the reference angle.
7
a) -100○
b)
10
2. Determine the quadrant in which the angle lies.
31
○
a) -2.15
b) 300
c)
12
Determine two coterminal angles (one pos., one neg.)
2
a) 
b) 700○
3
Even More Extra Practice
Evaluate each of the following.
1) cos (150 ○)
 17 
4) sin  6 


2) sin (360 ○)
11
3) cos
6
 2 
5) sin   
 3 
5
6) sin 4
7) tan(240○)
8) csc(-225○)
9) cot(20π/3)
10) sec(- π/4)