Download Unit 7 Lesson 4 Notes: The 3 Trigonometric Ratios

Unit 7 Lesson 4 Notes: The 3 Trigonometric Ratios
Name
Learning Targets: I CAN; 1) identify the sine, cosine, and tangent ratios of an acute angle of a right triangle. 2) set up
sine, cosine, or tangent ratio proportions to solve for missing side lengths of right triangles.3) change calculator mode to
degree mode and access the 3 trigonometric functions.
VOCABULARY
Trigonometric ratio
Let ABC be a right triangle with acute A. The sine of A, cosine of A, and tangent of A (written sin A,
cos A, and tan A) are defined as follows:
Sine A, sin A =
length of leg opposite 
=
length of hypotenuse
Cosine A, cos A =
length of leg adjacent to 
=
length of hypotenuse
length of leg opposite  A =
length of leg adjacent to  A
Tangent A, tan A =
In exercises 1 – 6, use MPQ at the right.
1. Name the side opposite M .
_______________
2. Name the side adjacent to M . _______________
3. Name the side opposite Q .
_______________
4. Name the side adjacent to Q .
_______________
Q
M
5. Name the hypotenuse of MPQ . _______________
P
6. Name the acute angles of MPQ . _______________
Target 1 – Identify sine, cosine, and tangent ratios.
Use the definitions of the three trigonometric ratios to complete each statement.
7. sin A = _______
8. sin B = ________
9. sin C = ________
cos A = _______
cos B = ________
cos C = ________
tan A = _______
tan B = ________
tan C = ________
R
t
o
a
T
T
Y
r
A
B
y
O
c
e
b
C
t
E
Find the sine, the cosine, and the tangent of  A and  B . Keep all answers in simplified fraction form!
10. B
11. C
10
B
12
5
12.
13
8
21
B
29
C
20
A
C
A
6
A
A
B
A
B
A
B
Sine:
________ ________
Sine:
________ ________
Sine:
________ ________
Cosine:
________ ________
Cosine:
________ ________
Cosine:
________ ________
Tangent: ________ ________
Tangent: ________ ________
Tangent: ________ ________
Target 2 - Set up and solve sine, cosine, or tangent ratio proportions.
First: identify which trig ratio to use in order to solve for the desired variable. Second: write this proportion
with all the information provided in the diagram. Last: solve the proportion.
Find the value of each variable in the diagram. Round to the nearest tenth.