the trigonometric functions we will be looking at sine cosine tangent
TRANSCRIPT
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The Trigonometric Functions we will be
looking at
SINE
COSINE
TANGENT
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The Trigonometric Functions
SINE
COSINE
TANGENT
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SINE
Pronounced “sign”
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Pronounced “co-sign”
COSINE
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Pronounced “tan-gent”
TANGENT
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Prounounced “theta”
Greek Letter q
Represents an unknown angle
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oppositehypotenuse
SinOpp
Hyp
Leg
adjacent
CosAdj
Hyp
Leg
TanOpp
Adj
Leg
Leg
hypotenuseopposite
adjacent
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We need a way to remember all of these ratios…
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Old Hippie
Old Hippie
SomeOldHippieCameAHoppin’ThroughOurApartment
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SOHCAHTOA
Old Hippie
Old Hippie
SinOppHypCosAdjHypTanOppAdj
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Finding sin, cos, and tan.
(Just writing a ratio or decimal.)
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Find the sine, the cosine, and the tangent of angle A.
Give a fraction and decimal answer (round to 4 places).
hyp
oppA sin
8.10
9 8333.
hyp
adjA cos
8.10
6 5556.
adj
oppA tan
6
9 5.1
9
6
10.8
A
Shrink yourself down and stand where the angle is.
Now, figure out your ratios.
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Find the sine, the cosine, and the tangent of angle A
A
24.5
23.1
8.2
hyp
oppA sin
5.24
2.8 3347.
hyp
adjA cos
5.24
1.23 9429.
adj
oppA tan
1.23
2.8 3550.
Give a fraction and decimal answer (round to 4 decimal places).
Shrink yourself down and stand where the angle is.Now, figure out your ratios.
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Finding a side.(Figuring out which ratio to use
and getting to use a trig button.)
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Ex: 1 Figure out which ratio to use. Find x. Round to the nearest tenth.
5520 m
x
20
55tanx
m 6.28x
x55tan20tan 20 55 )
Shrink yourself down and stand where the angle is.
Now, figure out which trig ratio you have and set up the problem.
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Ex: 2 Find the missing side. Round to the nearest tenth.
72
80 ft
x
x
8072tan
ft 26x
8072tan x
72tan
80x
tan 80 72 = ( ) )Shrink yourself down and stand where the angle is.Now, figure out which trig ratio you have and set up the problem.
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Ex: 3 Find the missing side. Round to the nearest tenth.
24
283 mx 283
24sinx
m 1.115x
x24sin283Shrink yourself down and stand where the angle is.
Now, figure out which trig ratio you have and set up the problem.
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Ex: 4 Find the missing side. Round to the nearest tenth.
4020 ft x
2040cos
x
ft 3.15x
x40cos20
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Finding an angle.(Figuring out which ratio to use and getting
to use the 2nd button and one of the trig buttons.)
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Ex. 1: Find . Round to four decimal places.
9
17.2
Make sure you are in degree mode (not radians).
9
2.17tan
2nd tan 17.2 9
3789.62
)
Shrink yourself down and stand where the angle is.Now, figure out which trig ratio you have and set up the problem.
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Ex. 2: Find . Round to three decimal places.
23
7
Make sure you are in degree mode (not radians).
23
7cos
2nd cos 7 23
281.72
)
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Ex. 3: Find . Round to three decimal places.
400
200
Make sure you are in degree mode (not radians).
400
200sin
2nd sin 200 400
30)
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When we are trying to find a sidewe use sin, cos, or tan.
When we are trying to find an angle we use sin-1, cos-1, or tan-1.