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Side Relationships in Special Right Triangles & Exact Values of The Trigonometric Functions.

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Presentation on theme: "Side Relationships in Special Right Triangles & Exact Values of The Trigonometric Functions."— Presentation transcript:

1 Side Relationships in Special Right Triangles & Exact Values of The Trigonometric Functions

2 Side Relationships in Special Right Triangles The 45° – 45 ° – 90 ° Theorem In a 45° - 45° - 90° triangle the hypotenuse is times as long as either leg. x 45° Example: Find the value of x in the triangle. hyp = leg hyp = 5 Therefore, x =

3 Side Relationships in Special Right Triangles The 30° – 60 ° – 90 ° Theorem In a 30° - 60° - 90° triangle the hypotenuse is 2 times as long as the shorter leg. The longer leg is times as long as the shorter leg. x 30° y 60° 20 Example: Find the value of x and y in the triangle. hyp = 2 shorter leg longer leg = shorter leg 20 = 2 yx = = y

4 Exact Values of The Trigonometric Functions There are certain angles for trigonometric functions which have exact values 0°, 90°, 180°, 270°, 30°, 45°, and 60° 0°0° 30 ° 45 ° 60 ° 90 ° Sin01 Cos10 Tan01undefined

5 Exact Values of The Trigonometric Functions Example: Find the exact values of the six trigonometric functions of 0°. Solution: Begin by drawing an angle of 0°, and choose any point that would lie on the terminal side. (3, 0) is one such point. x = 3 y = 0 r = 3 (3,0) x y

6 Homework Do #1 – 7 odd numbers only on page 235 from Section 7.4 and #1 and 2 on page 238 from Section 7.5 for Tuesday June 9 th


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