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TRIGONOMETRY
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TAN
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FUNCTIONS POSITIVE HERE
FUNCTIONS POSITIVE HERE
FUNCTIONS POSITIVE HERE
FUNCTIONS POSITIVE HERE
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W H A T’ S U P
In this learning modular, you will be reviewing for the
upcoming Exam.
This is meant to be a study tool so that you can succeed on
the examination. Everything on here will be in your Exam.
There will be a short quiz on each section, take it and study
the questions. Questions like those will be what your exam
will consist of.
MAY THE ODDS BE EVER IN YOUR FAVOR
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SOHCAHTOA
CLICK ME
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TRIANGLES
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SOHCAHTOA
SOHCAHTOA is an mnemonic commonly used in trigonometry to find a
missing side or angle in a right triangle. SOHCAHTOA can only be used
with RIGHT triangles, no others.
SOHCAHTOA stands for Sin Opp Hyp Cos Adj Hyp Tan Opp Adj
Fun Fact: SOHCAHTOA could also stands for
Some Old Hippo Caught Another Hippo Tripping Over Alligators
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SOHCAHTOA
HYP
Θ
SOH
I
N
P
P
Y
P
SIN(Θ) = OPP
HYP
OPP
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To find the SIN of a function, you take
the side opposite the given (or desired)
angle and divide it by the hypotenuse
(the side across from the box).
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EXAMPLE
1) You are walking through a field and
see a ant hill with dozens of little ants
walking up it. You can measure that the
ant hill is 12 cm off the ground and it is
15 cm to the edge of the opening. How
far do the ants actually walk to get into
their ant hill?
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EXAMPLE
SIN(Θ)=
56°
X
12 cm
OPP
HYP
15
X
15
SIN(56)
SIN(56)=
X=
X=18.0933 cm
15 cm
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SOHCAHTOA
Θ
ADJ
HYP
CAH
O
S
D
J
Y
P
COS(Θ) = ADJ
HYP
To find the COS of a function, you take the side
adjacent (between the angle and the box) the
given (or desired) angle and divide it by the
hypotenuse (the side across from the box).
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EXAMPLE
2) Your father is letting you help hang
Christmas lights this year. He leans the
13 foot ladder against the house. You
know that you are 9 feet away from the
house. At what height is the top of the
ladder?
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EXAMPLE
COS(Θ)= ADJ
HYP
43°
13 ft
X
COS(43)= 13
X=13COS(43)
X
X=9.5076 ft
9 ft
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SOHCAHTOA
TOA
Θ
ADJ
A
N
P
P
D
J
TAN(Θ) =
OPP
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OPP
ADJ
To find the TAN of a function, you take the
side opposite the given (or desired) angle
and divide it by the adjacent side (the side
between the angle and the box).
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EXAMPLE
3) An airplane just flew from Orlando, FL
to Chicago, IL and it is coming in for
landing. The pilots have decreased their
height from 26 km to 6 km. If it takes a
total distance of 16 km to land, how far
along the runway did it travel?
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EXAMPLE
OPP
ADJ
Y
TAN(23)= 6
TAN(Θ)=
65°
16 km
6 km
X=6 TAN(23)
X=12.8670 km
Y
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TRIANGLES
A triangle is one of the basic shapes in geometry. It has three corners
and three edges (angles and sides).
Fun Fact: Triangles can be found in EVERY shape you could think of,
even CIRCLES
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about each triangle?
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EQUALATERAL
All of the three angles and all of the
three sides are the same.
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ISOSCELES
Two of the three angles and two of the
three sides are the same.
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SCALENE
None of the three angles and none of
the three sides are the same.
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RIGHT
One angle MUST be 90° and the other
two must, together, add up to 90°.
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OBTUSE
One angle MUST be greater than 90°
and the other two must, together,
must make up the difference.
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ACUTE
One angle MUST be less than 90° and
the other two must, together, make up
the difference.
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TRIANGLE QUIZ
What kind of triangle is this?
A) Right
B) Equilateral
C) Obtuse
D) Acute
108°
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CORRECT!!
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INCORRECT
GOOD TRY!
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QUESTION AGAIN.
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TRIANGLE QUIZ
What kind of triangle is this?
30°
A) Right
B) Equilateral
C) Obtuse
D) Acute
60°
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TRIANGLE QUIZ
65°
What kind of triangle is this?
A) Trapezoid
B) Equilateral
70°
45°
C) Scalene
D) Acute
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TRIANGLE QUIZ
60°
What kind of triangle is this?
A) Right
B) Equilateral
60°
60°
C) Obtuse
D) Acute
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TRIANGLE QUIZ
What kind of triangle is this?
A) Isosceles
3 in
6 in
B) Obtuse
C) Scalene
4 in
D) Square
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YOU PASSED THE TRIANGLE
QUIZ!
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SOHCAHTOA QUIZ
What is the trigonometric
function of this triangle?
25°
A) SIN(25)=5.67/X
B) COS(25)=X/5.67
Y
C) SIN(25)=X/5.67
D) TAN(25)=X/Y
X
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SOHCAHTOA QUIZ
8.56 cm
64°
What is the trigonometric
function of this triangle?
Z
X
A) COS(64)=X/8.56
B) SIN(64)=8.56/Z
C) TAN(54)=X/8.56
D) COS(64)=8.56/Z
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SOHCAHTOA QUIZ
What is the trigonometric
function of this triangle?
20°
Z
Y
A) TAN(20)=6.33/Y
B) COS(20)=6.33/Z
C) SIN(20)=Z/6.33
D) COS(20)=Y/Z
6.33 km
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SOHCAHTOA QUIZ
6.45 cm
X
Z
44°
Solve for the missing variables
in this triangle.
A) X=6.55cm
Z=10.56cm
B) X=6.68cm
Z=9.45cm
C) X=6.68cm
Z=8.97cm
D) X=8.97cm
Z=6.68cm
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6.45 cm
ANSWERS 1
X
Z
44°
TO SOLVE FOR X:
TAN(44)=6.45/X
X TAN(44)=6.45
X=6.45/TAN(44)
USE YOUR CALCULATOR
X=6.679170524cm
ROUND TO TWO DECIMAL POINTS
X=6.68cm
TO SOLVE FOR Z:
COS(44)=6.45/Z
Z COS(44)=6.45
Z=6.45/COS(44)
USE YOUR CALCULATOR
Z=8.966555162cm
ROUND TO TWO DECIMAL POINTS
Z=8.97cm
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SOHCAHTOA QUIZ
Solve for the missing variables
in this triangle.
Y
A) X=5.26ft
Y=10.55ft
B) X=6.22ft
Y=7.26ft
C) X=4.66ft
Y=7.18ft
D) X=7.18ft
Y=4.66ft
33°
X
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Y
ANSWERS 2
33°
X
TO SOLVE FOR X:
COS(33)=X/8.56
8.56COS(33)=X
USE YOUR CALCULATOR
X=7.179020062ft
ROUND TO TWO DECIMAL POINTS
X=7.18ft
TO SOLVE FOR Y:
SIN(33)=Y/8.56
8.56SIN(33)=Y
USE YOUR CALCULATOR
Y=4.66211014ft
ROUND TO TWO DECIMAL POINTS
Y=4.66ft
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SOHCAHTOA QUIZ
7.84 m
54°
Solve for the missing variables
in this triangle.
Z
X
A) X=5.66m
Z=26.33m
B) X=10.79m
Z=13.34m
C) X=13.34m
Z=10.79m
D) X=5.00m
Z=13.35m
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7.84 m
54°
Z
X
ANSWERS 3
TO SOLVE FOR X:
TAN(54)=X/7.84
7.84TAN(54)=X
TO SOLVE FOR Z:
COS(54)=7.84/Z
Z COS(54)=7.84
Z=7.84/COS(54)
USE YOUR CALCULATOR
USE YOUR CALCULATOR
X=10.79083426m
Z=13.33820467m
ROUND TO TWO DECIMAL POINTS ROUND TO TWO DECIMAL POINTS
X=10.79m
Z=13.34m
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QUESTION AGAIN.
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SOHCAHTOA QUIZ!
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CONGRATULATIONS!!!
YOU MADE IT THROUGH THE HUNGER GAMES
JUST KIDDING
THIS MODULAR SHOULD HELP YOU STUDY FOR
THE EXAM AND GET AN A+++++ SO TRY GOING
OVER IT AGAIN SOMETIME BEFORE THE EXAM.