1. SOHCAHTOA Can only be used for a right triangle
If you don’t have a right triangle, you may have to add a line or 2 to make one!
Sine, Cosine, and Tangent each represent a FRACTION
If you are given…
2 sides, you can find the angle, θ
1 side and 1 angle, you can find a second side
Pythagorean theorem, a² + b² = c²
Use to find missing side when given 2 sides
C = hypotenuse

2. Hypotenuse is always across from the right angle!
SOHCAHTOA
Hypotenuse is always across from the right angle!

3. SOHCAHTOA

4. SOHCAHTOA If θ = a, Which is the opposite side?
Which is the adjacent side?
If θ = b,

5. SOHCAHTOA How to solve using a calculator Remember…
If given an angle and a side, use sin
If given 2 sides, use sin-1
Make sure to close the parentheses after entering the angle into the function!
Remember…
Sine and cosine will always be greater than 0 and less than 1

6. SOHCAHTOA
If you are not comfortable rearranging the equations, remember these triangles…
sin θ h o
cos θ h a
tan θ a o
To solve, simply cover up what you are trying to find
Finding opposite:
o = sinθ x h
Finding hypotenuse:
h = a/cosθ

7. SOHCAHTOA Steps to solving:
Label the sides of your triangle (opp, adj, hyp)
Tick the information you have been given
Tick the information you want to know
Decide whether to use sin, cos, or tan
Solve for your unknown
May need to rearrange equation
Can use triangle method

8. Practice Calculate the length of side BC.
Calculate the length of side AB.

9. Practice
Calculate x

10. Practice
Calculate the angle x

11. Vectors Vector: A quantity having direction as well as magnitude
Scalar: A quantity having only magnitude, not direction
Magnitude  size
Direction  angle, north, south, east, west, north of east, etc.

12. Vectors
In physics, we deal with various quantities that depend both on size/magnitude and direction.
Displacement, velocity, acceleration, force, etc.
It is important to know how to properly manipulate vectors.
Vector addition
Vector resolution

13. Vectors Specs Magnitude gives length of vector Example: 5 m
Direction tells which way the vector is acting (θ)
Always measured from the tail-end of the vector!
Example: 57° north of east, 41° above the horizontal
Tip: end of vector where it ends (arrow end)
Tail: end of vector where it originates
ALWAYS represented by an arrow!
6 m
Tip θ
Tail

14. Vectors Specs A vector can be moved anywhere in space as long as…
It maintains the same magnitude
It maintains the same direction

15. Vector Addition Methods:
Parallelogram method
Graphical method
Tip-to-Tail method
We will use the tip-to-tail method
When we add 2 or more vectors, the answer is called the resultant
The resultant also has magnitude and direction

16. Vectors Practical Examples:
If you want to row straight across a river when a current is flowing you must point the bow slightly upstream
A pilot must allow for the wind speed and direction when piloting an aircraft
A kicker in football must allow for the wind speed and direction when kicking a field goal
Rugby forwards are more effective if they push the scrum from behind

17. Vector Addition
In some situations, we need to determine the overall effect due to 2 vectors simultaneously acting on an object.
This is why we need to know how to add vectors
For example, imagine a boat traveling across a river.

18. Vector Addition Which way should you pull?
Now imagine that you and a friend want to pull a box along the road. (To make life easy lets imagine that the road is smooth – no friction). The box has two ropes fixed to it and you each take hold of one of them
If you both pull in the same direction with the same force the box will accelerate quickly (d) but if you pull in opposite directions with the same force you would expect the box to stay still and this is what would happen (e).
If you were stronger than your friend then the box would move the way you were pulling but not as fast if you pulled on your own (f).
(d)
(e)
(f)

19. Vector Addition Tip-to-tail method
Arrange vectors so that the tail of one vector is connected to the tip of the other vector
Draw the “resultant” vector from the tail of the first vector to the tip of the second vector (start to finish)
If drawn to scale, use a ruler and protractor to determine the magnitude and direction of the resultant vector.
Start
Finish

20. Vector Addition
Let’s practice arranging vectors tip-to-tail and drawing the resultant.
Let’s see how the resultant changes according to the 2 vectors being added.
Note: Any number of vectors can be added using the tip-to-tail method.

21. Vector Addition If the vectors act perpendicular to each other…
You can use the Pythagorean theorem, sine, cosine, and tangent to determine the magnitude and direction of the resultant.
Start
Finish

22. Practice
Two tractors try to rescue a cow that is trapped in a ditch. One pulls along the ditch with a force of 500 N and the other pulls at a right angle to the ditch with a force of 250 N. What is the combined force on the cow and in which direction will the cow move?

23. Practice
An airplane is traveling south to north at 350 m/s. There is a crosswind blowing west to east at 50 m/s. Find the final speed of the aircraft due to the crosswind and its engines (magnitude and direction).

24. Practice
A river flows at 5 m/s north to south. A boat is trying to cross the river east to west at a speed of 22 m/s. Find the overall speed of the boat due to the current and its engine (magnitude and direction).

25. Vector Resolution
Sometimes in Physics, you will be given a resultant vector and in turn will need to find its x and y components.
X component: travels ONLY in horizontal direction
Y component: travels ONLY in vertical direction
Resultant
Y-component
X-component

26. Vector Resolution When resolving a vector,
“complete the right triangle”
Note the length of the x component
Note the length of the y component
If you know the magnitude and direction of the resultant vector you may use sine, cosine, and tangent to determine the magnitude of the x and y component vectors.

27. Vector Resolution
When resolving a vector into its horizontal (x) and vertical (y) components…
First draw the vector and its components
Create the RIGHT triangle
Label θ
The horizontal (x) component equals:
Cos(θ) x hypotenuse
The vertical (y) component equals:
Sin(θ) x hypotenuse
Don’t forget to include direction with each component.

28. Vector Resolution Special cases:
A perfectly vertical vector has a horizontal component of ZERO.
θ = 90°, cos(90) = 0
A perfectly horizontal vector has a vertical component of ZERO.
θ = 0°, sin(0) = 0

29. Practice
Resolve a 42 N vector acting at 30° above the horizontal into its horizontal and vertical components.
Resolve a 75 N vector acting at 65° north of west into its horizontal and vertical components.
Resolve a 10 N vector acting at 15° below the horizontal into its horizontal and vertical components.
Resolve a 981 N vector acting at 85° west of south into its horizontal and vertical components.