TrigonometryHypotenuse

Opp

osite

Adjacent

TrigonometryHypotenuse

Opposite

Adj

acen

t

cos

sintan

cos

sin

adjacent

opposite

hypotenuse

adjacent

hypotenuse

opposite

Mnemonic device : SOH CAH TOA

N

E

10 km

52 °

38 °

10 km [E 38°N]

10 km [N 52°E]

SCALARS

# and unit

DISTANCE

SPEED

--

TIME

...

MASS (and other sizes)

WORK / ENERGY, ...

VECTORS

#, unit, and direction

DISPLACEMENT

VELOCITY

ACCELERATION

--

...

FORCE, MOMENTUM,

IMPULSE, ...

Length “ L ”

L si

n θ

L cos θ

ADDING VECTORS

Separate each vector into its components. Put all your Xs together and all your Ys together. Find how much left-right and how much up-down. Now, make it back into one big vector – use Pythagoras and Trig.

30°

40°

L =

16 m

L = 9 m16

cos

30°

16 sin 30° 9 cos 40°

9 sin 40°

16 c

os 3

0°=

13.8

56

16 sin 30°=8 9 cos 40°=6.894

9 sin 40°=5.785

13.8

56 m

8 m 6.894 m

5.785 m

VERTICAL HORIZONTAL

13.856 – 5.785 = 8.071

8 + 6.894 = 14.894

14.894 m

8.07

1 m

16.94 m

94.16894.14071.8 22

45.28)542.0(tan

894.14

071.8tan

1

16.94 m

Remember, the original problemwas: