
What does the unit circle tell us?
Presentation
•
Mathematics
•
10th Grade
•
Practice Problem
•
Easy
+2
Standards-aligned
Shalynne Orth
Used 21+ times
FREE Resource
4 Slides • 15 Questions
1
2
The triangle at the right is a right triangle, and θ is in standard position.
3
Fill in the Blanks
Type answer...
4
Match
Using θ as a reference angle, mark the triangle sides as Opp, Adj, and Hyp.
Label these on the triangle on your paper.
x
y
OP
Adj
Opp
Hyp
Adj
Opp
Hyp
5
Match
Now, use the given triangle to represent sinθ and cosθ in terms of the variables given in the diagram.
1y=y
1x=x
1
sinθ
cosθ
OP
sinθ
cosθ
OP
6
Drag and Drop
In terms of x and y, what does tanθ equal?
tanθ=
In terms of sinθ and cosθ, what does tanθ equal?
tanθ=
7
8
Dropdown
Reference angle =
9
Dropdown
Reference angle =
10
Drag and Drop
Thinking about how sine, cosine, and tangent relate to (x,y) coordinate pairs on the unit circle, find the quadrants where:
sine is positive:
sine is negative:
11
Drag and Drop
Thinking about how sine, cosine, and tangent relate to (x,y) coordinate pairs on the unit circle, find the quadrants where:
cosine is positive:
cosine is negative:
12
Drag and Drop
Thinking about how sine, cosine, and tangent relate to (x,y) coordinate pairs on the unit circle, find the quadrants where:
tangent is positive:
tangent is negative:
13
Dropdown
Try to remember these results without looking at the unit circle.
sin(3π)=
sin(67π)=
cos(45π)=
cos(−3π)=
14
The unit circle is a great tool for finding the exact value of trig functions, but it is not your only tool. Sometimes it is still convenient to think of using right triangles.
15
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16
Dropdown
Given that the missing side has length 3,
sinθ=
17
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18
Multiple Choice
Suppose you know that for a particular angle, cosθ=54 . The related triangle is shown.
If we know that 23π<θ<2π (i.e., the angle lies between 23π radians and 2π radians), what quadrant on the unit circle is the angle θ in?
I
II
III
IV
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