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

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**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. Example: Find the value of x in the triangle. hyp = leg hyp = Therefore, x = x 45°

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**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. Example: Find the value of x and y in the triangle. hyp = 2 shorter leg longer leg = shorter leg 20 = 2 y x = 10 10 = y x 30° 20 y 60°

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**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° 30° 45° 60° 90° Sin 1 Cos Tan undefined

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**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 y x (3,0)

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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 9th

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Pythagorean Theorem Converse Special Triangles. Pythagorean Theorem What do you remember? Right Triangles Hypotenuse – longest side Legs – two shorter.

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