Introduction to Trigonometry

1
Introduction to Trigonometry

• Right Triangle Trigonometry

2
Topic 4
Use Trig Ratios to Determine Angles
3
Determining Angles

• Instead of determining a ratio when you know an
  angle (which is all youve been doing so far),
  you can also go the other direction
• If you know a trig ratio, you can determine the
  size of the angle.

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Determining Angles
Determining Angles

• Check out this statement
• sin A 0.866

There exists only one angle where taking the
opposite side divided by the hypotenuse gives you
0.866
That angle is 60 degrees.
On some calculators, you have the press the 2nd
function key, then the sin key, type 0.866 and
press the key. Again, your answer will be
close to 60 degrees.
To get that answer, type 0.866 on your
calculator, press the 2nd function key, then
press the sin key. (It will be close to 60
degrees)
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Determining Angles
Determining Angles

• Here is another one
• cos A 0.707

There exists only one angle where taking the
adjacent side divided by the hypotenuse gives you
0.707
That angle is 45 degrees.
To get that answer, type 0.707 on your
calculator, press the 2nd function key, then
press the cos key. (It will be close to 45
degrees)
If your calculator operates differently, press
the 2nd function key first, then press the cos
key, type-in 0.707, then press .
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Determining Angles
Determining Angles

• One more
• tan A 0.577

There exists only one angle where taking the
opposite side divided by the adjacent gives you
0.577
That angle is 30 degrees.
To get that answer, type 0.577 on your
calculator, press the 2nd function key, then
press the tan key. (It will be close to 30
degrees)
If your calculator operates differently, press
the 2nd function key first, then press the tan
key, type-in 0.577, then press .
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Determining Angles
Determining Angles

• Try these problems using your calculator.
• Write each answer to the nearest tenth of a
  degree.
• sin A 0.65
• cos A 0.5
• tan A 1.2
• Click to see the answers.

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Determining Angles
Determining Angles

• Try these problems using your calculator.
• Write each answer to the nearest tenth of a
  degree.
• sin A 0.65 A 40.5
• cos A 0.5 A 60
• tan A 1.2 A 50.2
• Click to see the answers.

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Review

• Lets review what you should know by now.

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Review
Review

• Given a reference angle, correctly name the sides
  of a right triangle using the terms hypotenuse,
  opposite side, and adjacent side.

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Review
Review

• Name the three basic trig functions and their
  correct arrangements.

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Review
Review

• Determine the sin, cos, and/or tan of a given
  angle using your calculator.

cos 40 ?
0.766
sin 75 ?
0.9659
tan 10 ?
0.176
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Review
Review

• Given a ratio, determine the size of an angle.

tan A 0.355
A 19.5
cos A 0.5
A 60
sin A 0.866
A 60