Download Pythagoras: Starter

Trigonometry: Starter
1) Find the Sin
Cos
Tan
functions on your calculator
2) Check your calculator is in degrees (DEG) or (D)
Use mode to change DEG – RAD – GRAD
Use your calculator to find… (answer to 3dp if needed)
3) Sin 30 =
4) Cos 30 =
5) Tan 45 =
6) Sin 60 =
7) Cos 60 =
8) Tan 135 =
9) Sin 28 =
10) Cos 77 =
11) Tan 90 =
Trigonometry: Introduction A
Hypotenuse
length (h)=
30°
Side length (a) =
Calculate
length( a )

length( h)
Cos 30 =
Trigonometry: Introduction B
Hypotenuse
length (h)=
Side
length
(o) =
40°
Calculate
length( o )

length( h)
Sin 40 =
Trigonometry: Introduction C
Side
length
(o) =
35°
Side length (a) =
Calculate
length( o )

length( a )
Tan 35 =
Trigonometry: Putting it together A
1 metre
25°
We know that
length(a )
 Cos 25
length( h)
So if (h)  1 then length(a )  Cos 25
x metres
Or simply
4 metres
25°
x metres
x  Cos 25
Trigonometry: Putting it together B
x
metres
1 metre
We know that
34°
length(o)
 Sin 34
length( h)
So if (h)  1 then length(o)  Sin 34
Or simply
x
metres
12 metres
34°
x  Sin 34
Trigonometry: Putting it together C
We know that
x
metres
29°
1 metre
x
metres
42 metres 29°
length(o)
 Tan 29
length(a )
So if (h)  1 then length(o)  Tan 29
Or simply
x  Tan 29
Trigonometry: Rules
Use
Soh Cah Toa
Hypotenuse
(longest side)
h
(opposite
side)
o
θ
(adjacent side)
a
(o)
(a)
(o)
Opposite
Adjacent
Opposite
(h)
Sin θ Hypotenuse
(h)
Cos θ Hypotenuse
(a)
Tan θ Adjacent
Hypotenuse
(longest side)
Trigonometry: Steps
1) Label the triangle
2) Which two important sides?
3) Select the trig rule Soh Cah Toa
4) Write the rule triangle
5) Put in known values
6) Cover unknown value and solve
7) Working calculation
8) Answer sensible?
12
9) Units & rounding
xm
66°
4.5 m
h
(opposite
side)
o
θ
(adjacent side)
a
cm
x cm
20°
Sin & Cos problems
Beta pg 276 Ex 19.6
Trigonometry: Practice A
Beta pg 277 Ex 19.7
Simple triangle problems
Beta pg 278 Ex 19.6
Word & picture problems
Tan problems
Beta pg 281 Ex 19.9
Beta pg 281 Ex 19.10
Beta pg 282 Ex 19.11
Mixed problems
Beta pg 282 Ex 19.12
Trigonometry: Practice B
Sin & Cos problems
Beta pg 285 Ex 20.2
Simple triangle problems
Beta pg 285 Ex 20.3
Word & picture problems
Mixed problems
Beta pg 290 Ex 20.5
Word & picture problems
Beta pg 292 Ex 20.6
Trigonometry: Finding the angle
Hypotenuse
(longest side)
h
(opposite
side)
θ
o
6m
(adjacent side)
a
θ˚
4m
(o)
Opposite
(a)
Tan θ Adjacent
12 cm
16 cm
θ°
1) Find the marked angle in the triangle.
400 m
θ°
600 m
2) An aeroplane takes off and climbs in a straight line. If it flies 5000m
through the air and climbs to a height of 1200m find the angle of climb.
3) A ship leaves port and sails north for 2.4 km then east for 5 km. Find the
bearing the now is from the port
Beta: pg 297 Ex 21.3
pg 298 Ex 21.4
Extension: pg 300 Ex 21.5