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Trigonometry Basics

- Right Triangle Trigonometry

(No Transcript)

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 specifies these two sides of the

triangle, and they must be arranged as shown.

sin A

hypotenuse

opposite

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 0.7315 sin ?
- then sin-1 (0.7315) ?
- Solve for ? if sin ? 0.2419

Cosine function

Cosine Function

- The next trig function you need to know is the

cosine function (cos)

cos A

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 0.9272 cos ?
- then cos-1 (0.9272) ?
- Solve for ? if cos ? 0.5150

Tangent function

Tangent Function

- The last trig function you need to know is the

tangent function (tan)

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

Tangent Function

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

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

Inverse Tangent Function

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

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

Review

- The sin function

sin A

A

Review

Review

- The cosine function.

cos A

A

Review

Review

- The tangent function.

tan A

A

Most Common Application

r

y

?

x

Review

Review

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

Review

Review

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

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,

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?

?