Warm – up: Find the missing measures.
Write all answers in radical form.
45°
30°
x
7
10
z
45°
w
60°
y
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…
Some
Old
Hippie
Came
A
Hoppin’
Through
Our
Old Hippie Apartment
SOHCAHTOA
Old Hippie
Sin
Opp
Hyp
Cos
Adj
Hyp
Tan
Opp
Adj
Finding sin, cos, and tan
SOHCAHTOA
Opp
Sinq 
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
6
opp
9
sin A 


.
8333
hypo 10.8
adj
6
cos A 

hypo 10.8
opp
tan A 
adj
9

6
 .5555
 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 


cos q 
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
tan A 
adj
8.2

23.1  .3550
Word Problems…
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?
?
71.5°
50
Opp
tan 71.5°
Hyp
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
• To find the distance d from a house on shore to
a house on an island, a surveyor measures the
distance between points A and B as shown.
Using an instrument called a transit, he finds
the measurement of B .
• What is the distance
between the 2 houses?
• To find the distance d from a house on
shore to a house on an island, a surveyor
Draw a picture.
measures the distance between points A
Label it with what
and B as shown. Using an instrument
you know.
called a transit, he finds the measurement
Identify what you
of B.
need to find.
• What is the distance
Find the right
between the 2 houses?
triangle – (if there
SOLVE IT!
1.
2.
3.
4.
isn’t one, make
one!).
5. Solve using right
triangle trig.
Ratios.
Solve the problem: