Transcript Document

The Trigonometric Functions
we will be looking at
SINE
COSINE
TANGENT
The Trigonometric Functions
SINE
COSINE
TANGENT
SINE
Prounounced
“sign”
COSINE
Prounounced
“co-sign”
TANGENT
Prounounced
“tan-gent”
Greek Letter q
Prounounced
“theta”
Represents an unknown angle
Opp
Sin 
Hyp
hypotenuse
Adj
Cos 
Hyp
Opp
Tan 
Adj
q
adjacent
opposite
opposite
We need a way
to remember
all of these
ratios…
Old
Hippies
Are
High
On
Old Hippie Acid
SOHCAHTOA
Old Hippie
in
pp
yp
os
dj
yp
an
pp
dj
Finding sin, cos, and tan
SOHCAHTOA
Opp
Hyp
Adj
Cosq 
Hyp
8
10
4

5
10
8
3
6

10
5
q
Opp 8  4
Tanq 
Adj 6 3
6
Find the sine, the cosine, and the tangent of angle A.
Give a fraction and decimal answer (round to 4 places).
10.8
9
A
9
opp

sin A 

.
8333
hypo 10 .8
adj
6
cos A 

hypo 10 .8
 .5555
6
opp
tan A 
adj
9

6
 1 .5
Find the values of the three trigonometric functions of q.
?
5
4
q
Pythagorean Theorem:
(3)² + (4)² = c²
5=c
3
opp 4
adj 3
opp 4




sin q 
cosq 
tan
q
hyp 5
hyp 5
adj 3
Find the sine, the cosine, and the tangent of angle A
B
Give a fraction and
decimal answer (round
to 4 decimal places).
24.5
8.2
A
23.1
opp  8.2
sin A 
 .3347
24
.
5
hypo
23 .1
adj

cos A 
hypo 24 .5  .9429
opp
8 .2
tan A 

adj
23 .1  .3550
Finding a side
Ex.
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?
Opp
tan 71.5°
Hyp
?
71.5°
50
y
tan 71.5° 
50
y = 50 (tan 71.5°)
y = 50 (2.98868)
y  149.4 ft
Ex. 5
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?
cos 60°
x (cos 60°) = 200
200
60°
x
x
X = 400 yards