Given that and find the value of the cos θ Warm-Up: January 16, 2014 5 4 sin 2 2 3
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Given that and
find the value of the cos θ
Warm-Up: January 16, 2014
5
4sin
22
3
Homework Questions?
Memorize it! Quiz 1st week of 2nd semester
◦ 8 minute time limit◦ All or nothing◦ 20 points
There are a lot of patterns We will go over all of the patterns before the
quiz
Trig Value Table
Right Triangle Trigonometry
Section 4.3
A right triangle has a 90˚ angle and two acute angles
Right Triangles
a = length of side opposite of θ
b = length of side adjacent to θ
c = length of the hypotenuse
A
B
Cθ
Trigonometric Functions
adjacent
opposite
hypotenuse
adjacent
hypotenuse
opposite
tan
cos
sin
SOH-CAH-TOA
More Trigonometric Functions
opposite
adjacent
adjacent
hypotenuse
opposite
hypotenuse
cot
sec
csc
Find the value of each of the trigonometric functions of θ.
Example 1
3
4
c
A
B
Cθ
Find the value of each of the trigonometric functions of θ.
You-Try #1
5
12
c
A
B
Cθ
Pythagorean triples are integer side lengths of a right triangle
3-4-5 5-12-13 7-24-25 8-15-17 And many more And any multiple of any of them
(such as 6-8-10)
Pythagorean Triples
Degrees
Radians
sin cos tan
30˚
45˚
60˚
Trig Values of Special Angles
6
4
3
2
1
2
2
2
3
2
3
2
2
2
1
3
3
3
1
Page 461 #1-19 odd No calculator
Assignment
In Exercises 1-8, use the Pythagorean Theorem to find the length of the missing side of each right triangle. Then, find the value of each of the six trigonometric functions of θ.
First Few Problems
9
12
A
B
Cθ
1) 3)
21
29
A
B
Cθ
10
5)26
A
B
Cθ
Find the value of each of the trigonometric functions of θ.
Warm-Up: January 17, 2014
a
15
17
A
B
Cθ
Homework Questions?
The value of a trig function of an angle is equal to the value of the cofunction of the complement of the angle
If θ is in radians, replace 90˚ with
Cofunctions
2
90seccsc90cscsec
90tancot90cottan
90sincos90cossin
Find a cofunction with the same value as the given function.
Example 4
5csc)
9
2cot)
19sin)
c
b
a
Find a cofunction with the same value as the given function.
You-Try #4
11
2tan)
7cos)
42sec)
c
b
a
All scientific and graphing calculators should have buttons for sin, cos, and tan.
Most do not have csc, sec, and cot. Make sure that your calculator is set to the
correct angle measure (degrees or radians) TI-83: Press [MODE] and make sure the
correct one of “Radian” or “Degree” is highlighted
Trig Functions on TI-83
The angle formed by a horizontal line and the line of sight to an object that is above the horizontal line is the angle of elevation.
The angle formed by a horizontal line and the line of sight to an object that is below the horizontal line is the angle of depression.
Angles of Elevation & Depression
angle of depression
Sighting the top of a building, a surveyor measured the angle of elevation to be 24˚. The transit is 5 feet above the ground and 250 feet from the building. Find the building’s height (to the nearest foot).
Example 5
At a certain time of day, the angle of elevation of the sun is 39˚. A tree casts a shadow 37 feet long. Find the tree’s height (to the nearest foot).
You-Try #5
Page 462 #21-33 odd, 43-49 odd Calculator required
Assignment
In Exercises 21-28, find a cofunction with the same value as the given expression.
First Few Problems
5
2cos)27
9tan)25
25csc)23
7sin)21
At a certain time of day, the angle of elevation of the sun is 59˚. A tree casts a shadow 24 feet long. Find the tree’s height (to the nearest foot).
Warm-Up: January 27, 2014
Homework Questions?
Clear everything off of your desk except a pencil and eraser.
5 minute time limit All or nothing Must be turned in by the end of 5 minutes Do NOT begin until instructed to do so. Any talking while any quiz is out will result
in a zero.
Unit Circle Quiz!
Clear everything off of your desk except a pencil and eraser.
5 minute time limit
Unit Circle Quiz!
If , then “Theta equals the inverse sine of x” Other inverse trig functions follow the same
format TI-83: [2nd] [sin]
Inverse Trig Functions
xsin x1sin
The Washington Monument is 555 feet high. If you stand ¼ mile away (1320 feet), and look at the top, what is the angle of elevation (to the nearest degree)?
Example 6
A telephone pole is 55 feet tall. A guy wire 80 feet long is attached from the ground to the top of the pole. Find the angle between the wire and the pole to the nearest degree.
You-Try #6
Page 462 #35-42 ALL
Assignment
In Exercises 35-38, use a calculator to find the value of the acute angle θ to the nearest degree.
In Exercises 39-42, use a calculator to find the value of the acute angle θ in radians, rounded to three decimal places.
Assignment Problems
0307.26tan)386252.4tan)37
8771.0cos)362974.0sin)35
5117.0tan)424169.0tan)41
9499.0sin)404112.0cos)39
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