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Radians, Degrees, Trig and the Unit Circle
Contributed by: Miles
60°
120°
135°
150°
210°
30° is a reference angle for:
(Select all that apply)
225°
240°
300°
315°
330°
30°
120°
135°
150°
210°
60° is a reference angle for:
Select all that apply.
225°
240°
300°
315°
330°
60°
120°
135°
150°
210°
45° is a reference angle for:
Select all that apply.
225°
240°
300°
315°
330°
π/6 is a reference angle for which three?
π/3
/3
/4
/6
/6
/4
/3
/3
11π/6
/4
π/3 is a reference angle for which three?
π/6
/3
/4
/6
/6
/4
/3
/3
11π/6
/4
π/4 is a reference angle for which three?
π/3
/3
/4
/6
/6
/4
/3
/3
11π/6
/4
The magnitude of the radius of a unit circle is
1
π
r
√3/2
√2/2
The sine of an angle is equal to
r
x
y
1
theta
How many degrees in a unit circle?
180
π
1
360
The cosine of an angle is equal to
1
x
y
theta
r
For the unit circle, the sine is zero at:
180 degrees
Both 0 and 180 degrees
0 degrees
90 and 270 degrees
neither 0 nor 180 degrees
For the unit circle, the cosine is 1 at:
0 degrees
270 degrees
180 degrees
90 degrees
Both 90 and 180 degrees
For the unit circle, if I add this many radians to an angle, the sin and cosine will remain the same
-π/2
π
π/2
The sine of 90 degrees equals
-√2/2
1
0
√2/2
1/2
The cosine of 45 degrees equals
√2/2
45
-√2/2
1/2
√3/2
390 degrees is co-terminal with
30 degrees
-390 degrees
330 degrees
-30 degrees
The sine of π is
undefined
1
0
√3/2
180 degrees
The tan of π is
undefined
1
0
√3/2
180 degrees
π radians is co-terminal with which two?
-π radians
1/2 radians
3π radians
3π/2 radians
2π radians
3π/4 radians equivalent to:
3π/2 radians
45 degrees
135 degrees
315 degrees
225 degrees
Sine and Cosine are both negative in quadrant
III
IV
I
II
  • 22. How many radians in a unit circle?
A) 2π
B) 3π
C) π/2
D) π
E) 3π/2
  • 23. 180 degrees is equal to
A) 2π radians
B) 360 degrees
C) π/2 radians
D) π radians
The cosine is negative and the sine is positive in quadrant
III
I
II
IV
The cosine of 225 degrees equals
45
√3/2
√2/2
-√2/2
1/2
-390 degrees is co-terminal with
-30 degrees
330 degrees
-330 degrees
-390 degrees
  • 27. 270 degrees is equal to
A) 3π/2 radians
B) 90 degrees
C) 2π radians
D) π/2 radians
The cosine is negative and the sine is positive in quadrant:
III
II
IV
I
Drag the parts of a triangle into the correct location 
to set up the trig ratio. 
sin(θ)=
hypotenuse
?
opposite
?
Not used in sin function
adjacent
?
Drag the parts of a triangle into the correct location 
to set up the trig ratio. 
cos(θ)=
hypotenuse
?
adjacent
?
Not used in cos function
opposite
?
Drag the parts of a triangle into the correct location 
to set up the trig ratio. 
tan(θ)=
adjacent
?
opposite
?
Not used in tan function
hypotenuse
?
Drag the parts of a triangle into the correct location 
to set up the trig ratio. 
tan(θ)=
cosθ
?
sinθ
?
Match the radian measure to the correct position around the unit circle. 
Drag and drop your answers onto the Circle
7π/6
?
5π/6
?
π
?
5π/4
?
3π/4
?
4π/3
?
2π/3
?
3π/2
?
π/2
?
5π/3
?
π/3
?
7π/4
?
π/4
?
11π/6
?
π/6
?
?
?
Match the coordinate point to the correct position around the unit circle. 
Drag and drop your answers onto the Circle
(0, 1)
?
(1/2, √3/2)
?
(√2/2, √2/2)
?
(√3/2, 1/2)
?
(1, 0)
?
What is the value of cos(5π/3)?
What is the value of tan(3π/4)?
What is the value of sin(π/3)?
√3/2
?
1/2
?
-1
?
What is the exact value of sin (7π/4)?
What is the exact value of tan(7π/4)?
What is the exact value of cos (7π/4)?
√2/2
?
-√2/2
?
-1
?
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