Download 9.6: Special Angles in Right Triangles

Section 9.6 Special Right Triangles
Algebra 2/Trigonometry
9.6: Special Angles
in Right Triangles
The 30-60-90 Triangle
60°
1
2
30°
3
Chapter 9: Trig Part I
1
Section 9.6 Special Right Triangles
Algebra 2/Trigonometry
(1) Find all trigonometric ratios
using both acute angles.
60°
2
1
30°
sin 30° =
cos 30° =
1
2
3
3
2
1
cos 60° =
2
sin 60° =
3
2
1
3 tan 60° = 3
tan 30° =
=
3
3
The 45-45-90 Triangle
45°
2
1
45°
1
Chapter 9: Trig Part I
2
Section 9.6 Special Right Triangles
Algebra 2/Trigonometry
(2) Find all trigonometric ratios
using the acute angle.
45°
2
1
45°
1
2
2
2
1
2
cos 45° =
=
2
2
sin 45° =
1
=
tan 45° = 1
Finding Exact Values of Trigonometric Functions
Find the exact value of each expression:
(1) sin 30° + cos 60°
=
1 1
2
+
= =1
2 2
2
(2) sin 30° + tan 60° ଶ
ଶ
1
1+2 3
=
+ 3 =
2
2
13 + 4 3
=
4
Chapter 9: Trig Part I
ଶ
3
Section 9.6 Special Right Triangles
Algebra 2/Trigonometry
Finding Exact Values of Trigonometric Functions
Find the exact value of each expression:
(3) cos 180° + sin 270°
= −1 + (−1)
= −2
(4) tanଶ 60° + sin 180°
=
3
ଶ
+0
=3
Finding Exact Values of Trigonometric Functions
Find the exact value of each expression:
(5)(sin 0°)(tan 30°) + cos 0°
= 0
3
+1 =1
3
(6)(sin 30°)(cos 60°) + (cos 30°) sin 60°
1 1
3
3
=
+
2 2
2
2
4
1
3
= =1
=
+
4
4
4
Chapter 9: Trig Part I
4
Section 9.6 Special Right Triangles
Algebra 2/Trigonometry
Ex 7)The value of: 2 sin 30° cos 30°
is equivalent to the value of which of the
following?
sin 60°
cos 60°
sin 90°
tan 30°
2 sin 30° cos 30° =
=2
=
1
2
3
2
3
2
Homework:
pg. 380/ #4 - 30 even,
34 – 42 even
*NO calculator!
Chapter 9: Trig Part I
5