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Introduction to Trigonometry

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... has a built-in set of tables, so it can ... For example to evaluate sin 40 ... Type-in 40 on your calculator (make sure the calculator is in degree mode), then ... – PowerPoint PPT presentation

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Title: Introduction to Trigonometry


1
Introduction to Trigonometry
  • Right Triangle Trigonometry

2
Topic 3
The Three Trig Ratios
3
The sine ratio
  • The trig ratio that we just used (opp/hyp) is
    called the sine function.
  • It is abbreviated sin (but pronounced like
    sign).

4
Sine Function
  • When you talk about the sin of an angle, that
    means you are working with the opposite side, and
    the hypotenuse.

5
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
6
Sine Function
  • Here is the sin of some common angles
  • sin 0 0
  • sin 30 0.5
  • sin 45 0.707
  • sin 60 0.866
  • sin 90 1

Remember, all of these results come from forming
a right triangle using the indicated angle as the
reference angle...
and dividing the length of the opposite side by
the length of the hypotenuse. (Just like on the
charts you have been making.)
why is this one 90?
opposite is the hypotenuse for a 90
You would have the same number on both the top
bottom of the ratio
7
Sine Function
  • As you can see, you could spend years figuring
    out the sin ratios for every single angle.
  • Thats where the calculator comes in...

8
Sine Function
  • Your calculator has a built-in set of tables, so
    it can automatically tell you the sin of any
    angle.

9
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.

10
Sine Function
Sine Function
  • Try each of these on your calculator
  • sin 55
  • sin 10
  • sin 87
  • Click to see the answers.

11
Sine Function
Sine Function
  • Try each of these on your calculator
  • sin 55 0.819
  • sin 10 0.174
  • sin 87 0.999

12
Sine function
Sine Function
  • So to recap, the following shows the sin function
    for reference angle A

sin A
hypotenuse
opposite
A
13
Cosine function
Cosine Function
  • The next trig function you need to know is the
    cosine function (cos)

cos A
hypotenuse
A
adjacent
14
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.

15
Cosine Function
Cosine Function
  • Try these on your calculator
  • cos 25
  • cos 0
  • cos 90
  • cos 45
  • Click to see the answers.

16
Cosine Function
Cosine Function
  • Try these on your calculator
  • cos 25 0.906
  • cos 0 1
  • cos 90 0
  • cos 45 0.707

17
Tangent function
Tangent Function
  • The last trig function you need to know is the
    tangent function (tan)

tan A
opposite
A
adjacent
18
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.

19
Tangent Function
Tangent Function
  • Try these on your calculator
  • tan 5
  • tan 30
  • tan 80
  • tan 85
  • Click to see the answers.

20
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

21
Review
Review
  • Click to see the three trig functions you will be
    using in this course.
  • You need to memorize each one.
  • Use the memory device SOH CAH TOA

22
Review
  • The sin function

sin A
A
23
Review
Review
  • The cosine function.

cos A
A
24
Review
Review
  • The tangent function.

tan A
A
25
Review
Review
  • With what you know so far, you can compute any of
    these trig ratios
  • sin 30
  • cos 45
  • tan 20

26
Review
Review
  • With what you know so far, you can compute any of
    these trig ratios
  • sin 30 0.5
  • cos 45 0.707
  • tan 20 0.363
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