Trigonometry Basics

1
Trigonometry Basics

• Right Triangle Trigonometry

2
(No Transcript)
3
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.

4
Sine function

• Given a right triangle, and reference angle A

The sin function specifies these two sides of the
triangle, and they must be arranged as shown.
sin A
hypotenuse
opposite
A
5
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.

6
Sine Function
Sine Function

• Try each of these on your calculator
• sin 55
• sin 10
• sin 87

7
Sine Function
Sine Function

• Try each of these on your calculator
• sin 55 0.819
• sin 10 0.174
• sin 87 0.999

8
Inverse Sine Function
Inverse Sine Function

• Using sin-1 (inverse sin)
• If 0.7315 sin ?
• then sin-1 (0.7315) ?
• Solve for ? if sin ? 0.2419

9
Cosine function
Cosine Function

• The next trig function you need to know is the
  cosine function (cos)

cos A
hypotenuse
A
adjacent
10
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.

11
Cosine Function
Cosine Function

• Try these on your calculator
• cos 25
• cos 0
• cos 90
• cos 45

12
Cosine Function
Cosine Function

• Try these on your calculator
• cos 25 0.906
• cos 0 1
• cos 90 0
• cos 45 0.707

13
Inverse Cosine Function

• Using cos-1 (inverse cosine)
• If 0.9272 cos ?
• then cos-1 (0.9272) ?
• Solve for ? if cos ? 0.5150

14
Tangent function
Tangent Function

• The last trig function you need to know is the
  tangent function (tan)

tan A
opposite
A
adjacent
15
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.

16
Tangent Function
Tangent Function

• Try these on your calculator
• tan 5
• tan 30
• tan 80
• tan 85

17
Tangent Function
Tangent Function

• Try these on your calculator
• tan 5 0.087
• tan 30 0.577
• tan 80 5.671
• tan 85 11.430

18
Inverse Tangent Function

• Using tan-1 (inverse tangent)
• If 0.5543 tan ?
• then tan-1 (0.5543) ?
• Solve for ? if tan ? 28.64

19
Review
Review

• These are the only trig functions you will be
  using in this course.
• You need to memorize each one.
• Use the memory device SOH CAH TOA

20
Review

• The sin function

sin A
A
21
Review
Review

• The cosine function.

cos A
A
22
Review
Review

• The tangent function.

tan A
A
23
Most Common Application
r
y
?
x
24
Review
Review

• Solve for x
• x sin 30
• x cos 45
• x tan 20

25
Review
Review

• Solve for ?
• 0.7987 sin ?
• 0.9272 cos ?
• 2.145 tan ?

26
What if its not a right triangle? - Use the Law
of Cosines
The Law of Cosines In any triangle ABC, with
sides a, b, and c,
27
What if its not a right triangle?

• Law of Cosines - The square of the magnitude of
  the resultant vector is equal to the sum of the
  magnitude of the squares of the two vectors,
  minus two times the product of the magnitudes of
  the vectors, multiplied by the cosine of the
  angle between them.
• R2 A2 B2 2AB cos?

?