 Side Relationships in Special Right Triangles

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

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°

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°

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

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)

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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