Download Trigonometry of the Right Triangle

Trigonometry of the Right Triangle - 1
In your study of trigonometry of the right triangle, you will discover ways in which the similarity of triangles will provide
additional methods for measuring segments and angles indirectly.
G
Three right triangles are drawn to coincide
at vertex A. Since each triangle contains a
right angle as well as A , we know that all
three triangles are similar by AA AA .
ABC
ADE
E
C
AFG
Also, since corresponding sides of similar triangles
are in proportion, we can say:
F
D
B
Let’s recall our Trigonometric Ratios….. Remember “SOH CAH TOA”
Sine
sin
A
Cosine
cos
A
Tangent
tan
A
Reciprocal Functions
Cosecant
csc
A
Secant
sec
A
Cotangent
cot
A
A
1. Evaluate the six trigonometric functions of the given angle: (EXACT value)
G
E
C
15
10
6
9
5
3
A
F
A
D
A
B
4
8
12
sin A
sin A
sin A
cos A
cos A
cos A
tan A
tan A
tan A
csc A
csc A
csc A
sec A
sec A
sec A
cot A
cot A
cot A
2. Find the value. (Use your CALCULATOR. Round to the nearest thousandth, if necessary)
a.
tan 24
d. sec72
b. sin 30
c. cos 55
e. cot 52
f. csc 40
3. Given right
JKL below, find the EXACT value of:
4. Given right
ABC below, tan A
9 find the EXACT
12
value of:
K
B
a. sin L =
a. csc A =
17
9
b. sec L =
15
L
J
A
C
c. tan K =
8
b. cot A =
c. cos B =
12
Trigonometric Values for Special Angles
30o - 60o - 90o
45o - 45o - 90o
60°
45°
2x
x 2
1x
x
30°
45°
x 3
x
5. Find the EXACT value of the trigonometric functions:
sin 30
sin 60
sin 45
cos 30
cos 60
cos 45
tan 30
tan 60
tan 45
csc 30
csc 60
csc 45
sec 30
sec 60
sec 45
cot 30
cot 60
cot 45
6. Evaluate the six trigonometric functions of the given angle: (EXACT value)
B
B
a.
b.
60°
45°
14
7 2
16
8
45°
30°
C
C
A
8 3
sin 30
sin 60
sin 45
cos 30
cos 60
cos 45
tan 30
tan 60
tan 45
7 2
7. Find the measure of the given angle: *Use your trigonometric values of special angles*
a.
b.
B
B
x
8 2
16
10
5
x
C
m A
A
C
m B
A
A
Trigonometry – Worksheet 1
1.
Find the exact value of the six trigonometric functions of the given
x.
sin x
cos x
15
x
tan x
7
csc x
sec x
cot x
2.
Let x be an acute angle of a right triangle. Find the values of the other 5 trigonometric functions of x, if
13
.
sec x
5
x
3. Given right
sin x
csc x
cos x
sec x
tan x
cot x
ABC below, find the EXACT value of:
C
a. cos C =
5
b. csc C =
3
c. tan A =
B
A
4
d. sec A =
4. Find the value. (Use your CALCULATOR. Round to the nearest thousandth, if necessary)
a.
b. tan 70
sec 24
c. csc55
5. If one side of an equilateral triangle has a length of 6, what is the length of its altitude? Show work.
6. Find the measure of the given angle: *Use your trigonometric values of special angles*
a.
x
10
5 3
4 2
b.
x
4 2
7. Can the sin x ever be a value greater than 1? Explain.