Download Math 120 - Section 2.3

Math 120 - Cooley
Trigonometry
OCC
Section 2.3 – Computing the Values of Trigonometric Functions of Acute Angles
Right Triangles with Hypotenuse of length 1 formed with Acute Angles 30, 45, and 60.
Trigonometric Table of Values


(in Radians)

(in Degrees)
6

4

3
30°
45°
60°
sin
cos
tan
csc
sec
1
2
3
2
2
2
1
2
3
3
2
2 3
3
1
2
2
1
2 3
3
2
3
3
2
2
3
2
3
cot
3
How to approach learning your trigonometric values:
 Learn or be able to generate the values for sin and cos.
 All other values for tan, csc, sec, and cot can be derived based on their definitions in terms of sin
and cos.
 The values for the acute angles of

6
triangles and 45°–45°–90° triangles.
,

4
, and
 The values for the quadrantal angles of 0,

2

3
can be memorized or generated from 30°–60°–90°
,  , and
3
can be obtained from the coordinates of these
2
points on the unit circle.
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Math 120 - Cooley
Trigonometry
OCC
Section 2.3 – Computing the Values of Trigonometric Functions of Acute Angles
 Exercises: Find the exact value of each expression. Do not use a calculator.
1) 2sin 45  4cos30
2) tan

4
 cot
3) 4  tan 2

4

3
4) sec2 60  tan 2 45
 Exercises: Use a calculator to find the approximate value of each expression. Round your answer to two
decimal places.
5) cos14
6) cot 70
7) csc55
8) tan
5
12
9) sin
5
8
10) cos1
11) cos1
 Exercises:
12)
A person in a small boat, offshore from a vertical cliff known to be 100 feet in height, takes a sighting
of the top of the cliff. If the angle of elevation is found to be 30, how far offshore is the ship?
13)
A 22-foot extension ladder leaning against a building makes a 70 angle with the ground. How far up
the building does the ladder touch?
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Math 120 - Cooley
Trigonometry
OCC
Section 2.3 – Computing the Values of Trigonometric Functions of Acute Angles
 Exercises:
14)
While taking a ride in a hot-air balloon in Napa Valley, Francisco wonders how high he is. To find out,
he chooses a landmark that is to the east of the balloon and measures the angle of depression to be 54.
A few minutes later, after traveling 100 feet east, the angle of depression to the same landmark is
determined to be 61 Use this information to determine the height of the balloon.
15)
The CN tower, located in Toronto, Canada, is the tallest structure in the world. While visiting Toronto, a
tourist wondered what the height of the tower above the top of the sky pod is. While standing 4000 feet
from the tower, she measured the angle to the top of the Sky Pod to be 20.1. At this same distance, the
angle of elevation to the top of the tower was found to be 24.4. Use this information to determine the
height of the tower above the Sky Pod.
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