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

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.
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°

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°
30°
45°
60°
90°
Sin 1
Cos
Tan
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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 y x
(3,0)

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 9th 