presents let’s investigate extension the tangent ratio the sine ratio the cosine ratio the three...
TRANSCRIPT
Trigonometry means “triangle” and “measurement”.
AdjacentO
pp
osit
e
xx°°
hypotenuse
We will be using right-angled triangles.
For an angle of 30°, OppositeAdjacent
= 0.6
We write tan 30° = 0.6
Opposite
Adjacent is called the tangent of an angle.
Tan 25° 0.466
Tan 26° 0.488
Tan 27° 0.510
Tan 28° 0.532
Tan 29° 0.554
Tan 30° 0.577
Tan 31° 0.601
Tan 32° 0.625
Tan 33° 0.649
Tan 34° 0.675
Tan 30° = 0.577
Accurate to 3 decimal places!
The ancient Greeks discovered this and repeated this for all possible angles.
Now-a-days we can use calculators instead of tables to find the Tan of an angle.
TanOn your calculator press
Notice that your calculator is incredibly accurate!!
Followed by 30, and press
=
Accurate to 9 decimal places!
Tan x° =
Opp
Adj
Tan 60° =
h12
= h
12 x Tan 60°h =
12 x Tan 60°= 20.8m (1 d.p.)
Change side, change sign!
Copy this!
Example
6565°°
Tan x° =
Opp
Opp
AdjHyp cc
8m8mTan 65° =
c8
= c
8 x Tan 65°
c =
8 x Tan 65° = 17.2m (1 d.p.)
Adj
Change side, change sign!
= 1.5Tan x°How do we find x°?
We need to use Tan ⁻¹on the calculator.
2nd
Tan ⁻¹is written above Tan
Tan ⁻¹
To get this press
TanFollowed by
Example
3434°°
Sin x° =
Opp
Opp
Hyp
Hyphh
11c11cmm
Sin 34° =
h11
= h
11 x Sin 34°
h =
11 x Sin 34°
= 6.2cm (1 d.p.)
Change side, change sign!
=0.667 (3 d.p.)Sin x°
How do we find x°?
We need to use Sin ⁻¹on the calculator.
2nd
Sin ⁻¹is written above Sin
Sin ⁻¹
To get this press
SinFollowed by
Example4040°°
Cos x° =
Opp
Adj
Hyp
Hyp
bb
35m35mmm
Cos 40° =
b35
= b
35 x Cos 40°
b =
35 x Cos 40°
= 26.8mm (1 d.p.)
Adj
Change side, change sign!
Examplexx°°
Cos x° =
Opp
Adj
Hyp
Hyp SOH CAH TOA45cm45cm
Cos x° = 3445
= 0.756 (3 d.p.)Cos x°
x =
Cos ⁻¹0.756 =40.9° (1 d.p.)
Adj34cm34cm
Example 1
4040°°
Sin x° =
Opp
Opp
Hyp
Hyp
SOH CAH TOAhh
1515mm
Sin 40° =
h15
= h
15 x Sin 40°
h =
15 x Sin 40°
= 9.6m (1 d.p.)
Change side, change sign!
Example 23535°°
Cos x° =
Opp
Adj
Hyp
Hyp SOH CAH TOA
bb
23cm23cm
Cos 35° =
b23
= b
23 x Cos 35°
b =
23 x Cos 35°= 18.8cm (1 d.p.)
Adj
Change side, change sign!
Example 3
6060°°Tan x° =
Opp
Opp
Adj
Hyp SOH CAH TOAcc
15m15m
Tan 60° =
c15
= c
15 x Tan 60°c =
15 x Tan 60°= 26.0m (1 d.p.)
Adj
Change side, change sign!
Example 25050°°
Cos x° =
Opp
Adj
Hyp
Hyp SOH CAH TOA
7m7m
pp
Cos 50° =
7p
p=
p= 10.9m (1 d.p.)
Adj
Change sides, change signs!
Cos 50°
7
Example 3
5555°°Tan x° =
Opp
Opp
Adj
Hyp SOH CAH TOA9m9m
ddAdj
Tan 55° =
9d
d=
d= 6.3m (1 d.p.)
Change sides, change signs!
Tan 55°
9