Transcript File

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
(SOH)
hypotenuse
Adj
Cos 
Hyp
Opp
Tan 
Adj
(CAH)
q
adjacent
(TOA)
opposite
opposite
What’s the purpose of SOH CAH
TOA?
The Sine, Cosine and Tangent functions express
the ratios of sides of a right triangle.
We use this to find missing angles.
We can find an unknown angle in a right-angled
triangle, as long as we know the lengths of two of its
sides.
The function takes an angle and gives us the ratio, and
the inverse function takes the ratio to give us the angle
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
Sin =
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 
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
Now, find the actual measurement of angle A by using
the inverse
8.2
B
STOP: Make sure Mode
on your calculator is set
to “Degree” not “Radian”
24.5
A
23.1
sin-1 (8.2/24.5)= 19.6 degrees No matter how you do it, you should
get the same answer (and because we
(23.1/24.5)= 19.5 degrees have all 3 sides, it doesn’t matter
tan-1 (8.2/23.1)= 19.5 degrees which we choose)
cos-1
Check: Does it make sense? Lets check Angle B:
sin-1 (23.1/24.5)= 70.5 degrees
70.5 + 19.5 + 90 = 180 degrees. That works!
Finding a side
Ex.
A surveyor is standing 50 feet from the base of a
large tree. The surveyor measures the non-right
angle from the ground to the top of the tree as
71.5°. How tall is the tree?
tan 71.5°
?
71.5°
50
y
tan 71.5° 
50
y = 50 (tan 71.5°)
y = 50 (2.98868)
y  149.4 ft
Ex. 2
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