warm – up: find the missing measures. write all answers in radical form. 45° x w 7 60° 30° 10 y...
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Warm – up: Find the missing measures. Write all answers in radical form.
45°
45° x
w
7
60°
30°
10
y
z
The Trigonometric Functions we will be
looking at
SINE
COSINE
TANGENT
The Trigonometric Functions
SINE
COSINE
TANGENT
SINE
Pronounced “sign”
Pronounced “co-sign”
COSINE
Pronounced “tan-gent”
TANGENT
Pronounced “theta”
Greek Letter
Represents an unknown angle
oppositehypotenuse
SinOpp
Hyp
adjacent
CosAdj
Hyp
TanOpp
Adj
hypotenuseopposite
adjacent
We need a way to remember all of these ratios…
SomeOldHagCameAroundHereTakingOurApples
Finding sin, cos, and tan
6
8
10
SOHCAHTOA
10
8
10
6
6
8
CosAdj
Hyp
TanOpp
Adj
4
5
3
5
4
3
Hyp
OppSin
Find the sine, the cosine, and the tangent of angle A.
Give a fraction and decimal answer (round to 4 places).
hyp
oppAsin
8.10
9 8333.
hyp
adjAcos
8.10
6 5556.
adj
oppAtan
6
9 5.1
9
6
10.8
A
Find the values of the three trigonometric functions of .
4
3
? Pythagorean Theorem:(3)² + (4)² = c²
5 = c
opp
hyp 4
5
adj
hyp
3
5 opp
adj
4
3
sin cos tan
5
Find the sine, the cosine, and the tangent of angle A
A
24.5
23.1
8.2
hyp
oppAsin
5.24
2.8 3347.
hyp
adjAcos
5.24
1.23 9429.
adj
oppAtan
1.23
2.8 3550.
B Give a fraction and decimal answer (round to 4 decimal places).
Finding a side
A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree?
50
71.5°
?
tan 71.5°
tan 71.5°50
y
y = 50 (tan 71.5°)
y = 50 (2.98868)
149.4y ft
Ex.
Opp
Hyp
A person is 200 yards from a river. Rather than walk directly to the river, the person walks along a straight path to the river’s edge at a 60° angle. How far must the person walk to reach the river’s edge?
200
x
Ex. 5
60°
cos 60°
x (cos 60°) = 200
x
X = 400 yards