Trigonometry+All

8/8/2019 Trigonometry+All

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TrigonometryTrigonometryTrigonometryTrigonometry

Right angled trianglesRight angled triangles


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A triangle


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Opposite and Adjacent

are relative to the angle The 4cm side

is opposite toA

The 6cm side

is adjacentto A

The 6cm sideis opposite toB

The 4cm sideis adjacentto B


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S A ASine, Cosine & Tangent of

an angle


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SOH CAH TOA SOH

Some Old Houses (Sine of angle =Opposite side / Hypotenuse)

CAH Creak And Howl

(Cosine of angle = Adjacent side / hypotenuse)

TOA Through Out Autumn (Tangent of angle = Opposite side / adjacent side)


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TOASOH CAH TOA

Toms Old Auntie Tangent of angle = Opposite side / adjacent side

SOH Sat On Him

Sine of angle =Opposite side / Hypotenuse

CAH Cursing At Him

Cosine of angle = Adjacent side / hypotenuse


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SOH CAH TOA SOHSOH

Opposite side = sin (x)

times hypotenuse

Hypotenuse = opposite

side divided by sin (x)

Sin (x) = opposite side

divided by hypotenuse


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SOHCAH TOA CAHCAH

Adjacent side = cos (x)

times hypotenuse

Hypotenuse = adjacent

side divided by cos (x)

Cos (x) = adjacent side

divided by hypotenuse


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SOH CAHTOA TOATOA

Opposite side = tan (x)

times adjacent side

Adjacent side = opposite

side divided by tan (x)

tan (x) = opposite side

divided by adjacent side


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Problems for trigA stage, is to be built for a concert, it has to be 2m high so

the audience can see the show.The equipment needs to be pushed up onto the stage. Health

and safety rules say that a ramp must have a slope of nomore than 15 degrees.

The crew need to work out how far away from the stage tostart building the ramp.

m


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A stage, is to be built for a concert, has to be 2m high so theaudience can see the show.

The equipment needs to be pushed up onto the stage. Healthand safety rules say that a ramp must have a slope of nomore than 15 degrees.

The crew need to work out how far away from the stage tostart building the ramp.

m


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5.7)tan(

2

)tan(!!!

xx

oppadj

Put answer in context:

The ramp must start from at least 7.5m away from the stage


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From take-off, an aeroplane climbs atan angle of 20o. When the aeroplane has

flown 10km, what height has it

reached?

Distance from ground.

km


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Looking for opposite (distance fromground) got hypotenuse.

Must be Sine formula triangle

Distance from ground.

Distance from ground = sin (20) x 10

= 3.42 km from the ground

km


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Aplane flies 300km on a bearing of 132 0

from an airport. How far south and east is itfrom the airport. Give answer correct to 3 s.f.

North is always straight up your page for these questions..

Bearings are always measured from north around in aclockwise direction.


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Draw the problem and work out the angle at AThen choose which side you want to find first

then choose the formula triangle to suit.


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Distance South firstlooking for adjacent side therefore use

cosine formula triangle

kmadj 201300)48cos( !v!


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Distance Eastlooking for opposite side therefore use the

sine formula triangle

kmopp 223300)48sin( !v!


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Ratio just means the number youget when you divide one number by

anotherSimilar shapes havethe same angles so they have thesame angle ratios.

A

A1

A2

BC1 C2C

Sin(30) is always thesame number no

matter what size theopp or hyp

Cos(30) is always thesame number no

matter what size the

adj or hyp

Tan(30) is alwaysthe same number nomatter what size the

opp or adj


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Sine ratioSin(x)=opp / hyp

51.0)31sin( !

51.074.11

6

1.4

1.2!!!

hyp

opp

4.3 / 8.42 = ?


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To find the angle (x) when youknow sin (x) use the calculator

inverse sine function (sin-1) Sin (x) = 0.86

x = Sin-1 (0.86) = 59 0

Sin (x) = 0.35x = Sin-1 (0.35) = 21 0

Sin (x) = 0.45 , what is x ?Sin (x) = 0.91, what is x?

27 0

66 0


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Cosine ratiocos(x) = adj / hyp

Cos(30) = 0.86

86.054.11

10

62.4

4)30cos( !!!!

hyp

adj

16/18.46=?


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To find the angle (x) when youknow cos (x) use the calculator

inverse cosine function (cos-1)

Cos (x) = 0.86x = Cos-1 (0.86) = 31 0

Cos (x) = 0.35x = Cos-1 (0.35) = 70 0

Cos (x) = 0.45 , what is x ?

Cos (x) = 0.91, what is x?

63 0

24 0


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Tangent ratiotan(x) = opp / adj

Tan(30) =0.58

58.010

83.5

4

33.2

)30tan(!!!!

adj

opp

7.58 / 13 = ?


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To find the angle (x) when youknow tan (x) use the calculator

inverse tangent function (tan-1)

tan (x) = 0.86

x tan (0.86) = 41 0

tan (x) = 0.35x = tan-1 (0.35) = 19 0

tan (x) = 0.45 , what is x ?

tan (x) = 0.91, what is x?

24 0

42 0


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A tourist lift to the top of a cliff travels 23m fromground to the top of the cliff. The height from

ground to the top of the cliff is 20m what is the

angle of elevation?

Sketch the problem Choose a formula triangle

We have opposite andhypotenuse must be sine

formula triangle


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Looking for the angle BAC.Work out the sine of the angle BAC

then use inverse sine to get angle.

869565.02320)sin( !!A

oA 60)869565.0(sin

1!!


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Health and Safety stipulates that a ladder held up at the sideof a wall must have an angle of elevation between 700 and 800

to be considered safe. The height to be reached is 2.4m but

the only ladder available is 4.9m will it be classed as safe?

4897959.09.4

4.2)sin( !!A

oA 29)4897959.0(sin

1!!

Not safe


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Find angles A and B?

We know all sidesso ANY formula triangle will be ok to use.


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832.021.7

6)cos( !!A

oA 34)832.0(sin

1!!


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y

!! 6.06

4)tan(A

oA 34)6.0(tan

1!!

y


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554785.021.7

4)cos( !!B

oB 56)554785.0(sin

1!!


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5.14

6)tan( !!B

oB 56)5.1(tan

1!!

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