 To add vectors you place the base of the second vector on the tip of the first vector  You make a path out of the arrows like you’re drawing a treasure map  The answer vector (called the resultant) is the vector that connects the start of the path to the end of the path.  Measure the resultant with a ruler to find the magnitude.

 3 90° + 6 0° = ? resultant (answer vector)

 This method of adding vectors is called the “Tip-to-tail method” since you put the tail of the second vector on the tip of the first vector resultant (answer vector)

 When adding perpendicular vectors you use the Pythagorean Theorem a b c

 When adding vectors by drawing you use a protractor and measure the angle of the resultant.  When adding vectors mathematically you use Trigonometry to find the direction of the resultant.

 Sine (sin)  Cosine (cos)  Tangent (tan)  Each function uses two sides of a right triangle  The angle we are using is labeled with the Greek letter “theta” or “θ”

θ hypotenuse opposite adjacent

 Angles are measured from the +x-axis Quadrant 1: 0°-90°Quadrant 2: 90°-180° Quadrant 3: 180°-270°Quadrant 4: 270°-360° Your calculator will give you the angle to the closest part of the x-axis. You need to add or subtract to adjust the angle to the ranges shown. y x

A hiker hikes 22 km East, then 11 km North. Determine the magnitude and direction of the hiker’s displacement. θ 22 km 11 km resultant

A hiker hikes 11 km East, then 22 km North. Determine the magnitude and direction of the hiker’s displacement. θ 22 km 11 km resultant Your calculator must be in degrees mode!