Warm-Up 1 Find the value of x..

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Presentation transcript:

Warm-Up 1 Find the value of x.

Warm-Up 1 Find the value of x.

Trigonometric Ratios I Objectives: To discover the three main trigonometric ratios To use trig ratios to find the lengths of sides of right triangles

Summary hypotenuse side opposite Θ side adjacent Θ

SohCahToa

Example 3 Find the values of the six trig ratios for α and β.

Activity: Trig Table Step 5: Finally, let’s check your values with those from the calculator. For sin, cos, and tan Make sure your calculator is set to DEGREE in the MODE menu. Use one of the 3 trig keys. Get in the habit of closing the parenthesis.

Example 4 To the nearest meter, find the height of a right triangle if one acute angle measures 35° and the adjacent side measures 24 m.

Example 5 To the nearest foot, find the length of the hypotenuse of a right triangle if one of the acute angles measures 20° and the opposite side measures 410 feet.

Example 6 Use a special right triangle to find the exact values of sin(45°) and cos(45°).

Example 7 Find the area of a regular octagon with a side length of 6 inches. 22.5

Example 8 Find the value of x to the nearest tenth. x =

Find the values of 𝑤 and 𝑥

Challenge Problem Make a conjecture about how the sine and cosine of 30° angle are related.

Challenge Problem Make a conjecture about how the sine and cosine of 60° angle are related.

Challenge Problem Square ABCD in the diagram at the right has side length of 1, and midpoints of its sides are labeled P, Q, R, and S. Find the length of a side of the shaded square