9.5 The Sine & Cosine Ratios

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Presentation transcript:

9.5 The Sine & Cosine Ratios Trigonometric Ratio Sides: Opposite-Adjacent-Hypotenuse Ratio of Opposite Side to Hypotenuse Ratio of Adjacent Side to Hypotenuse

Remember, Trigonometric Ratios are constant for any given acute angle in a right triangle and are tabulated in the Table of Trigonometric Values

Example 2: Calculating Trigonometric Ratios Use your calculator to find the value of the trigonometric ratio. Round to the nearest hundredth. sin 52° Be sure your calculator is in degree mode, not radian mode. Caution! sin 52°  0.79

Calculating Trigonometric Ratios Use your calculator to find the value of the trigonometric ratio. Round to the nearest hundredth. cos 19° cos 19°  0.95

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Tangent Ratios for Special Right Triangles 5 Find sin 45, sin 60 and cos 30. Leave your answers in reduced radical form: Step 1: Draw 45-45-90 and a 30-60-90 right triangles and place the ratios for the sides on the triangles. 2 Step 2: Calculate the tangents

Check It Out! Example 7 What if…? Suppose a plane is at an altitude of 3500 ft and the angle of elevation from the airport to the plane is 29°. What is the line-of-sight distance between the airport and the plane?

Example 8: Problem-Solving Application The Pilatusbahn in Switzerland is the world’s steepest cog railway. Its steepest section makes an angle of about 25.6º with the horizontal and rises about 0.9 km. To the nearest hundredth of a kilometer, how long is this section of the railway track?

Lesson Quiz: Use a special right triangle to write each trigonometric ratio as a fraction. 1. sin 60° 2. cos 45° Use your calculator to find each trigonometric ratio. Round to the nearest hundredth. 3. tan 84° 4. cos 13°

Find each length. Round to the nearest tenth. 5. CB 6. AC Use your answers from Items 5 and 6 to write each trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth. 7. sin A 8. cos A 9. tan A

10.

11. A ramp has an angle of elevation of 20° 11. A ramp has an angle of elevation of 20°. It has a vertical height of 1.8 m. What is the length of ramp?