Transcript angles

Get a calculator!
Trigonometry
Trigonometry is concerned with the
connection between the sides and
angles in any right angled triangle.
Angle
The sides of a right -angled triangle are
given special names:
The hypotenuse, the opposite and the
adjacent.
The hypotenuse is the longest side and is
always opposite the right angle.
The opposite and adjacent sides refer to
another angle, other than the 90o.
A
A
There are three formulae involved in
trigonometry:
sin A=
cos A=
tan A =
S OH C AH T OA
Using trigonometry on the calculator
All individual angles have different sine, cosine
and tangent ratios (or decimal values).
Scientific calculators store information about
every angle.
We need to be able to access this
information in the correct manner.
Finding the ratios
The simplest form of question is finding the
decimal value of the ratio of a given angle.
Find:
1) sin 32
=
sin
32
2) cos 23
=
3) tan 78
=
4) tan 27
=
5) sin 68
=
=
Using ratios to find angles
We have just found that a scientific
calculator holds the ratio information
for sine (sin), cosine (cos) and
tangent (tan) for all angles.
It can also be used in reverse, finding
an angle from a ratio.
To do this we use the sin-1, cos-1 and
tan-1 function keys.
Example:
1. sin x = 0.1115 find angle x.
sin-1
(
shift
0.1115
=
)
sin
x = sin-1 (0.1115)
x = 6.4o
2.
cos x = 0.8988 find angle x
cos-1
(
shift
0.8988
cos
=
)
x = cos-1 (0.8988)
x = 26o
Trigonometry
Learning Objective:
To be able to use trigonometry to find the
unknown angle in a triangle.
To be able to use trigonometry to find an
unknown side in a triangle.
1.
H
14 cm
6 cm
A
C
We have been given
the adjacent and
hypotenuse so we use
COSINE:
Cos A =
adjacent
hypotenuse
Cos A = a
h
Cos C = 6
14
Cos C = 0.4286
C = cos-1 (0.4286)
C = 64.6o
2. Find angle x
3 cm
A
Given adj and opp
need to use tan:
x
opposite
Tan A = adjacent
8 cm
O
Tan A = o
a
Tan x = 8
3
Tan x = 2.6667
x = tan-1 (2.6667)
x = 69.4o
3.
10 cm
12 cm
Given opp and hyp
need to use sin:
opposite
Sin A = hypotenuse
y
o
h
sin x = 10
12
sin A =
sin x = 0.8333
x = sin-1 (0.8333)
x = 56.4o
1.
H
7 cm
k
A
30o
We have been given
the adj and hyp so we
use COSINE:
Cos A =
Cos A = a
h
Cos 30 = k
7
Cos 30 x 7 = k
6.1 cm = k
adjacent
hypotenuse
2.
We have been given
the opp and adj so we
use TAN:
50o
4 cm
A
Tan A =
r
O
Tan A = o
a
r
Tan 50 =
4
Tan 50 x 4 = r
4.8 cm = r
3.
k
O
H
12 cm
We have been given
the opp and hyp so we
use SINE:
Sin A =
25o
o
h
sin 25 = k
12
sin A =
Sin 25
x 12 = k
5.1 cm = k