1. Trigonometry

2. Sides and Angles Basic trigonometry is about things to do
with the different ANGLES in a right angle
triangle
Look at the angle labeled
OPPOSITE SIDE Opposite the angle
HYPOTENEUSE Opposite the right angle
ADJACENT The side next to the angle

3. Examples of labeling sides
O = Opposite
H = Hypotenuse
A = Adjacent H O x A O A
Another example H x

4. Ratio of sides OPP = Sine of the angle HYP ADJ = Cosine of the angle
OPP = Tangent of the angle
ADJ
SIN
on a calculator
COS
on a calculator
TAN
on a calculator
Try working out SIN 30 on your calculator,
you should get 0.5 as your answer

5. Finding a side using tangent
Remember
OPP = Tangent of the angle
ADJ
TAN
on a calculator
Example
Find x
Label sides (Opp, Hyp, Adj)
Since we want ‘Opp’ and we
know ‘Adj’, choose tan.
tan 50° = OPP
ADJ
= x 8
8 x tan 50° = x
X = 9.53cm to 3 s.f.
50°
8cm x

6. Finding a side using sine
Remember: OPP = Sine of the angle
HYP
SIN
on a calculator
Example
Find x
Label sides (Opp, Hyp, Adj)
Since we want ‘Opp’ and we know ‘Hyp’, choose sin
sin 42° = OPP
HYP
sin 42° = x 12
12 x sin 42° = x
X = 8.03 cm to 3 s.f.
42 °
12cm x

7. Finding a side using cosine
Remember: ADJ = Cos of the angle
HYP
COS
on a calculator
71 °
33cm x
Example
Find x
Label sides (Opp, Hyp, Adj)
Since we want ‘Adj’ and we know ‘Hyp’, choose cos
cos 71° = ADJ
HYP
cos 71° = x 33
33 x cos 71° = x
X = 10.7 cm to 3 s.f.

8. Finding the hypotenuse
Find x
Label sides
Cos 21° = adj
hyp
Cos 21° = 9 x
x x Cos 21 ° = 9
x = 9
Cos 21°
x = 9.64cm (3s.f.)
21°
9cm x
SOHCAHTOA

9. Finding the hypotenuse
Find x
Label sides
Sin 79° = opp
hyp
Sin 79° = 22 x
x x Sin 79 ° = 22
x = 22
Sin 79°
x = 22.4cm (3s.f.)
79°
22cm x
SOHCAHTOA

10. ( ) Finding an angle sin x = Opp Hyp Sin x = 7 11 x = Sin 7
Find x
sin x = Opp
Hyp
Sin x = 7 11
x = Sin
x = 39.5° (to 1 d.p.) x°
7 cm
11cm
( ) -1
Remember Sin x = OPP, Cos x = ADJ, Tan x = OPP
HYP HYP ADJ