find the missing measures. write all answers in radical form. 60° 30° 10 y z warm – up 3 45 y...
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Find the missing measures. Write all answers in radical form.
60°
30° 10
y
z
Warm – up
3
45y60
30x
45
23
33
y
x
5
35
y
z
Agenda for today
WedMore 5.2 & 5.3 and 5.4
Fri Test Unit #4
1.Notes SOHCAHTOA
2.CW/HW
1.Notes SOHCAHTOA
2.CW/HW Thur Sect 5.4 cont
and applications
Date: 09/29/09Questions over hw?
Standards:MA2G2:a: Discover the relationship of the trigonometric ratios for similar triangles.
Students will define and apply sine, cosine, and tangent ratios to right triangles.
The Trigonometric Functions we will be
looking at
SINE
COSINE
TANGENT
5.2 & 5.3
The Trigonometric Functions
SINE
COSINE
TANGENT
SINE
Pronounced “sign”
Pronounced “co-sign”
COSINE
Pronounced “tan-gent”
TANGENT
Prounounced “theta”
Greek Letter q
Represents an unknown angle
oppositehypotenuse
SinOpp
Hyp
Leg
adjacent
CosAdj
Hyp
Leg
TanOpp
Adj
Leg
Leg
hypotenuseopposite
adjacent
We need a way to remember all of these ratios…
Old Hippie
Old Hippie
SomeOldHippieCameAHoppin’ThroughOurApartment
SOHCAHTOA
Old Hippie
Old Hippie
SinOppHypCosAdjHypTanOppAdj
Finding sin, cos, and tan.
(Just writing a ratio or decimal.)
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.
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.
Finding a side.(Figuring out which ratio to use
and getting to use a trig button.)
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.
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.
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.
Ex: 4 Find the missing side. Round to the nearest tenth.
4020 ft x
2040cos
x
ft 3.15x
x40cos20
Finding an angle.(Figuring out which ratio to use and getting
to use the 2nd button and one of the trig buttons.)
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.
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
)
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)
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.