Download Sep 212:31 PM Sep 212:31 PM Sep 212:31 PM Sep 212:31 PM Sep

ADV MT 6.2
UNIT CIRCLE
Consider a right triangle, one of whose acute angles is θ. The three sides of the triangle are the hypotenuse, the side opposite θ , and the side adjacent to θ.
Ratios of a right triangle's three sides are used to define the six trigonometric functions. sine, cosine, tangent, cosecant, secant, and cotangent. These six functions are abbreviated sin, cos, tan, csc, sec, and cot, respectively. hypotenuse
opposite side
θ
adjacent side
Sep 21­2:31 PM
RIGHT TRIANGLE DEFINITION OF TRIGONOMETRIC FUNCTIONS
Let θ be an acute angle of a right triangle. The six trig
functions of θ are defined as follows.
Sep 21­2:31 PM
Evaluate the six trig functions of the angle θ shown in the right triangle.
θ
14
7
Sin θ = opp Cos θ = adj Tan θ = opp
hyp
hyp adj
Csc θ = 7√3
hyp Secθ = hyp Cot θ = adj
opp
adj opp
5
θ
12
Sep 21­2:31 PM
Sep 21­2:31 PM
If ϑ is an acute angle in a right triangle, find the remaining trig functions.
0o
30o
45o 60o 90o
sin
0
1/2
√2/2 √3/2 1
cos
tan
1
√3/2 √2/2 1/2 0
0
1/√3
1 √3 und
sin ϑ = 3/8
To get the reciprocal functions, csc, sec, cot, flip the fractions!
tan ϑ = 5/9
Evaluate.
Sep 21­2:31 PM
sin 60o
tan 30o
cos 45o csc 30o cot 90o
sec 45o
sin ∏/4 cos ∏/3 tan ∏/2 csc ∏/6
Sep 21­2:31 PM
1
For special angles in radians, look at denominator of fraction to determine reference angle
To evaluate using the calculator, be sure to have calculator in correct mode.
sin 72o
sec .38
Sep 28­2:45 PM
csc(π/9) cos3.1
Sep 22­12:46 PM
http://www.unitedstreaming.com/search/assetDetail.cfm?guidAssetID=10F24BE2­2751­43DA­
BFDF­92ABE00378A6&rand=F48EF35B­14C2­4000­B8DB96B7BB10CED9
Use the table to find the angle measure.
cot ϑ = 1 sec ϑ = 1/√3
sin ϑ = 1/2
cot 21o
SOLVE THE RIGHT TRIANGLE.
A
A = 36o, a = 16
c
b
C
a
B
B = 31o, a = 21
Use the calculator to find the angle measure in degrees.
cos ϑ = .8182
tan ϑ = .954 A = 47o, c = 14
Sep 22­12:46 PM
SOLVE THE TRIANGLE
Sep 21­2:31 PM
5
8
θ
8
17
θ
11
θ
15
Sep 19­9:13 AM
Sep 16­12:49 PM
2