Transcript Intro to Trigonometry

Trigonometry Basics
Right Triangle Trigonometry
Sine Function
• When you talk about the sin of an angle,
that means you are working with the
opposite side, and the hypotenuse of a
right triangle.
Sine function
• Given a right triangle, and reference angle A:
The sin function
opposite
sin A =
specifies these
hypotenuse
two sides of the
triangle, and
hypotenuse
they must be
arrangedopposite
as
shown.
A
Sine Function
• For example to evaluate sin 40°…
• Type-in 40 on your calculator (make sure
the calculator is in degree mode), then
press the sin key.
• It should show a result of 0.642787…
– Note: If this did not work on your calculator,
try pressing the sin key first, then type-in 40.
Press the = key to get the answer.
Sine Function
Sine Function
•
•
•
•
Try each of these on your calculator:
sin 55°
sin 10°
sin 87°
Sine
Function
Sine
Function
Try each of these on your calculator:
 sin 55° = 0.819
 sin 10° = 0.174
 sin 87° = 0.999

Inverse
Sine Function
Inverse
Sine Function
• Using sin-1 (inverse sin):
If
then
0.7315 =
sin-1 (0.7315) =
• Solve for θ if sin θ = 0.2419
sin θ
θ
Cosine
function
Cosine
Function

The next trig function you need to know
is the cosine function (cos):
cos A =
adjacent
hypotenuse
hypotenuse
A
adjacent
Cosine Function
Cosine Function
•
•
•
•
Use your calculator to determine cos 50°
First, type-in 50…
…then press the cos key.
You should get an answer of 0.642787...
– Note: If this did not work on your calculator,
try pressing the cos key first, then type-in 50.
Press the = key to get the answer.
Cosine Function
Cosine Function
•
•
•
•
•
Try these on your calculator:
cos 25°
cos 0°
cos 90°
cos 45°
Cosine
Function
Cosine
Function
Try these on your calculator:
 cos 25° = 0.906
 cos 0° = 1
 cos 90° = 0
 cos 45° = 0.707

Inverse Cosine Function
• Using cos-1 (inverse cosine):
If
then
0.9272 =
cos-1 (0.9272) =
• Solve for θ if cos θ = 0.5150
cos θ
θ
Tangent Function
function

The last trig function you need to know
is the tangent function (tan):
opposite
adjacent
tan A =
opposite
A
adjacent
Tangent Function
Use your calculator to determine tan
40°
 First, type-in 40…
 …then press the tan key.
 You should get an answer of 0.839...

 Note:
If this did not work on your
calculator, try pressing the tan key first,
then type-in 40. Press the = key to get the
answer.
Tangent Function
Try these on your calculator:
 tan 5°
 tan 30°
 tan 80°
 tan 85°

Tangent Function
Try these on your calculator:
 tan 5° = 0.087
 tan 30° = 0.577
 tan 80° = 5.671
 tan 85° = 11.430

Inverse Tangent Function
• Using tan-1 (inverse tangent):
If
then
0.5543 =
tan-1 (0.5543) =
• Solve for θ if tan θ = 28.64
tan θ
θ
Remember SOHCAHTOA
• Sine is Opposite
divided by
Hypotenuse
• Cosine is Adjacent
divided by
Hypotenuse
• Tangent is Opposite
divided by Adjacent
• SOHCAHTOA!!!!!!
Table of Contents
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•
•
•
•
Examples
Question 1
Question 2
Question 3
Question 4
Example 1
If a = 3 and c = 6, what is the
measurement of angle A?
Answer: a/c is a sine relationship
with A.
Sine A = 3/6 = .5, from your
calculator, angle A = 30 degrees.
Example 2
• A flagpole casts a 100
foot shadow at noon.
Lying on the ground
at the end of the
shadow you measure
an angle of 25
degrees to the top of
the flagpole.
• How High is the
flagpole?
How do you solve this question?
• You have an angle, 25
degrees, and the length of the
side next to the angle, 100
feet. You are trying to find the
length of the side opposite the
angle.
• Opposite/adjacent is a tangent
relationship
• Let x be the height of the
flagpole
• From your calculator, the
tangent of 25 is .47
x
• .47 = 100
• x = (.47)(100), x = 47
• The flagpole is 47 feet high.
Question 1
• Given Angle A is 35 degrees, and b = 50
feet.
• Find c. Click on the correct answer.
• A. 61 feet
• B 87 feet
• C. 71 feet
GREAT JOB!
• You have an angle and an
adjacent side, you need to
find the hypotenuse. You
knew that the cosine finds
the relationship between the
adjacent and the
hypotenuse.
• Cosine 35 = 50/c, c Cosine
35 = 50,
• So c = 50/cos 35, or
approximately 61
Next question
Nice try
• You have an angle
and the adjacent side.
You want to find the
hypotenuse.
• What relationship
uses the adjacent and
the hypotenuse?
Back to
Question
Back to tutorial
Question 2
• If the adjacent side is 50, and the
hypotenuse is 100, what is the angle?
Please click on the correct answer.
• A. 60 degrees
• B. 30 degrees
• C. 26 degrees
Way to go!
• Given the adjacent
side and the
hypotenuse, you
recognized that the
adjacent divided by
the hypotenuse was a
cosine relationship.
• Cosine A = 50/100,
• A = 60 degrees
Next question
Nice try
• Given an adjacent
side and a
hypotenuse, what
relationship will give
you the angle?
Back to question
Back to tutorial
Question 3
• If the opposite side is 75, and the angle is
80 degrees, how long is the adjacent side?
• A. 431
• B. 76
• C. 13
Nice job
• You were given the
opposite side of 75 and
an angle of 80 degrees
and were asked to find
the adjacent side. You
recognized that this was
a tangent relationship.
• Tangent 80 = 75/b,
• b tangent 80 = 75,
• b=
= 13
75
tan 80
Next question
Nice Try
• You are given an
angle and the
opposite side, and
have been asked to
find the adjacent side.
What relationship
uses the opposite
side and the adjacent
side?
Back to question
Back to tutorial
Question 4:
If B = 50 degrees and b = 100
what is c?
B
B. 130
C. 84
c
________
A. 155
a
A ________ C
b
Nice try
• What is the
relationship between
B and b? And, what is
the relationship
between b and c?
Return to question
Return to tutorial
Great job!
• First, you recognized that
b is the opposite side
from B. Then, you
recognized that the
relationship between an
opposite side and the
hypotenuse is a sine
relationship.
• Sine 50 = 100/c, c Sine
50 = 100, c = 100/sine 50
= 130.
Go to next section
Congratulations
• You have learned how to use the 3 main
trig functions, you have learned which
functions are positive in which quadrants,
and you have learned values of sine,
cosine, and tangent for 5 standard angles.
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