Transcript SohCahToaPwrPt

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
Sinq 
Hyp
hypotenuse
Adj
Cosq 
Hyp
Opp
Tanq 
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
9
opp

sin A 
hypo 10.8  .8333
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 

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 
24.5  .9429
hypo
opp
tan A 
adj
8 .2

23.1  .3550
Let’s find the calculator
connections.
Draw a 30º-60º-90º to help you find sin 30º.
Now use your calculator to find sin 30º.
So… What is sin 45º? 1
What is cos 27º? .8910
What is tan 62º? 1.881
Can using the calculator help us
solve this problem?
In triangle PQR, m P = 90º, and
mQ = 35º. If PQ = 16, find the
lengths of the other two sides.
Can using the calculator help us
solve this problem?
In triangle PQR, m P = 90º, and
mQ = 35º. If PQ = 16, find the
lengths of the other two sides.
Q
PR
tan35 
35
16
16
16  tan35  PR
P
R PR  11.20
Can using the calculator help us
solve this problem?
In triangle PQR, m P = 90º, and
mQ = 35º. If PQ = 16, find the
lengths of the other two sides.
16
Q
cos35 
35
QR
16
QR  cos35  16
P
R QR  16
cos35
QR  19.53
What about indirect
measurement?
• The angle of elevation of a kite
with respect to the ground is 79º.
If 100’ of string is holding
the kite to the ground,
how high is the kite
actually flying?
Solution:
• The angle of elevation of a kite with respect to the
ground is 79º. If 100’ of string is holding the kite
to the ground, how high is the kite flying?
h
sin 79 
100
100  sin 79  h
100’
98.16'
79º
h
You try….
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
x
71.5°
50
x
tan 71.5° 
50
x = 50 (tan 71.5°)
x = 50 (2.98868)
x  149.4 ft
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