Similar Triangles, Right Triangles, And The Definition Of The Sine, Cosine And Tangent Functions Of Angles Of A Right Triangle Worksheets With Answer Key
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43MPE Review
Section II: Trigonometry
Review similar triangles, right triangles, and the definition of the sine, cosine and tangent functions of
angles of a right triangle. In particular, recall that the corresponding sides of similar triangles are
proportional. Moreover, two triangles are similar if two angles of one are equal to two angles of the
other. Don't overlook the enormously important Pythagorean Theorem for right triangles,
2
2
2
(a
+ b
= c
).
You will need to use a scientific calculator for the trigonometry section of the Colorado State
University Mathematics Placement Examination. In particular, review how and when to use radian or
degree measure for angles, and how to evaluate trigonometric and inverse trigonometric functions.
ANGLES
θ
The angle
shown in the Figure T1 is in standard position;
i.e., its initial side is the positive x-axis and its terminal side
is a ray from the origin. The angle is positive if the rotation
is counter-clockwise, and negative if the rotation is clockwise.
Example: Estimate the degree and radian measures of the
θ
angle
in Figure T1.
Figure T1
θ
5
Solution: Angle
is formed by rotating a ray through
/
12
revolutions counterclockwise from the positive
x-axis. One full revolution counterclockwise forms
π
an angle of 360° or 2
radians. Therefore, the
measures of angle θ are
π
5
(
)
5
( )
5
π
°
=
°
=
360
150
or
2
.
12
12
6
Problems:
Figure T2
1. What is the approximate degree measure of the angle in
Figure T2?
2. What is the approximate degree and radian measures of
the angle in Figure T3?
Figure T3
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