D. Trigonometry D. Trigonometry Math 10: Foundations and Pre-Calculus

FP10.4 Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.

Key Terms:Key Terms:Find the definition

of each of the following terms:

Angle of Inclination

Tangent RatioSine RatioCosine RatioIndirect

Measurement

Angle of Elevation

Angle of Depression

1. 1. The Tangent RatioThe Tangent RatioFP10.4 Develop and apply the primary

trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.

1. 1. The Tangent RatioThe Tangent RatioRemember the Tan ratio?

What is the tan ratio and what do we use it for?

The value of the tangent ratio is usually expressed as a decimal that compares the lengths of the sides

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You can use a scientific calculator to determine the measure of an acute angle when you know the value tan ratio

The tan-1 or Inv tan on your calculator does this for you

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PracticePracticeEx. 2.1 (p. 74) #1-20

#6-23

2. 2. Calculating Length with Calculating Length with Tangent RatioTangent RatioFP10.4 Develop and apply the primary

trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.

The tangent ratio is a powerful tool we can use to calculate the length of a leg of a right triangle

We are measuring indirectly when we measure this way

We can find the length of a leg of a triangle by setting up the tangent formula, as long as we have one of the acute angles and the legs

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Example 3Example 3

Practice Practice Ex. 2.2 (p. 81) #1-14

#1-4, 6-16

3. 3. Sine and Cosine RatiosSine and Cosine RatiosFP10.4 Develop and apply the primary

trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.

In a right triangle, the ratios that relate each leg to the hypotenuse depend only on the measure of the acute angle not the size of the triangle

These ratios are called the sine and cosine ratios

The sine ratio is written sin θ

The cosine ratio is written cos θ

The sine, cosine and tangent ratios are called the primary trig ratio

The values of the trig ratios are often expressed as decimals

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PracticePracticeEx. 2.4 (p. 94) #1-15

#1-3, 5-17

4. 4. Using Sine and Cosine to Using Sine and Cosine to find Lengthfind LengthFP10.4 Develop and apply the primary

trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.

4. 4. Using Sine and Cosine to Using Sine and Cosine to find Lengthfind Length

Construct Understanding p. 97

We can use the sin and cos ratios to write an equation that we can solve to calculate the length of a leg in a right triangle

When the measure of one acute angle and the hypotenuse are know

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The sin and cosine ratios can be used to calculate the measure of the hypotenuse

When the measure of one acute angle and the length of one of the legs are known

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PracticePracticeEx. 2.5 (p. 101) #1-12

#1-14

5. 5. Applying TrigApplying TrigFP10.4 Develop and apply the primary

trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.

5. 5. Applying TrigApplying Trig

Construct Understanding p. 105

When we calculate the measures of all the angles and all the side lengths in a right triangle, we solve the triangles.

We can use any of the three primary trig ratios to do this.

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PracticePracticeEx. 2.6 (p. 110) #1-14

#1-2, 5-16

6. 6. Problems with More Problems with More Triangles Triangles FP10.4 Develop and apply the primary

trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.

6. 6. Problems with More Problems with More Triangles Triangles We can use Trig to solve

problems that can be modeled using right triangles

When one more right triangle is involved, we have to decide which triangle to start with

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Sometimes the right triangles are not even in the same plane

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Practice Practice Ex. 2.7 (p. 118) #1-14

#5-21