Download Side Relationships in Special Right Triangles & Exact

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 2 times as long as either leg.
Example: Find the value of x in the triangle.
x
45°
hyp =
hyp =
Therefore, x =
2  leg
2 5
5 2
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
3 times as long as the shorter leg.
Example: Find the value of x and y in the triangle.
x
30°
20
hyp = 2  shorter leg longer leg =
60°
y
20 = 2  y
x = 3  10
10 = y
x  10 3
3  shorter leg
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
0
1
2
2
2
3
2
1
Cos
1
3
2
2
2
1
2
0
Tan
0
3
2
1
3
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
y
side. (3, 0) is one such point.
x = 3 sin 0  0 cos 0  3
3
3
y=0
3
3
r = 3 csc 0  0 sec 0  3
 undefined
0
tan 0 
3
3
cot 0 
0
 undefined
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 