the trigonometric functions we will be looking at
DESCRIPTION
The Trigonometric Functions we will be looking at. SINE. COSINE. TANGENT. The Trigonometric Functions. SIN E. COS INE. TAN GENT. SIN E. Pronounced “sign”. COS INE. Pronounced “co-sign”. TAN GENT. Pronounced “tan-gent”. Greek Letter q . Prounounced “theta”. - PowerPoint PPT PresentationTRANSCRIPT
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The Trigonometric Functions we will be
looking at
SINECOSINE
TANGENT
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The Trigonometric Functions
SINECOSINE
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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q
oppositehypotenuse
Sin OppHyp
Leg
adjacent
Cos AdjHyp
Leg
Tan OppAdj
Leg Leg
hypotenuseopposite
adjacent
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We need a way to remember all of these ratios…
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Old Hippie
SomeOldHippieCameAHoppin’ThroughOurApartment
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SOHCAHTOA
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).
hypoppA sin
8.109
8333.
hypadjA cos
8.106
5556.
adjoppA tan
69
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
hypoppA sin
5.242.8
3347.
hypadjA cos
5.241.23
9429.
adjoppA tan
1.232.8
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
55tan x
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
72tan80
x
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
24sin x
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 q. Round to four decimal places.
9
17.2
Make sure you are in degree mode (not radians).
92.17tan q
q
2nd tan 17.2 9
3789.62q
)
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 q. Round to three decimal places.
23
7
Make sure you are in degree mode (not radians).
237cos qq
2nd cos 7 23
281.72q
)
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Ex. 3: Find q. Round to three decimal places.
400
200
Make sure you are in degree mode (not radians).
400200sin qq
2nd sin 200 400
30q)
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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.