Vector Addition using Trigonometry Describe how to add vectors graphically. How do you resolve a vector into components? How are the components used to accomplish vector addition? How do you change components to polar form? How is vector subtraction accomplished? How is vector multiplication accomplished? Describe the differences between scalar and vector products of vectors. Source: http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

Vector Addition using Trigonometry Notes: Remember that you can move a vector as long as you do not change its magnitude or direction. This may be necessary to find the opposite or adjacent side.

Vector Addition using Trigonometry Adding Vectors - using trigonometry Case 1: (Ax is the side adjacent to angle Θ) Ax = cos(θ) x A, since Ax is the side adjacent to angle θ, A is the hypotenuse and cos = adj/hyp Ay = sin(θ) x A, since Ay is (parallel to) the side opposite angle θ, A is the hypotenuse and sin = opp/hyp Note: Depending on the quadrant, you may have to add a – sign in front of Ax and/or Ay

Vector Addition using Trigonometry Adding Vectors - using trigonometry Case 2: (Ay is the side adjacent to angle Θ) Ax = sin(θ) x A, since Ax is (parallel to) the side opposite to angle θ, A is the hypotenuse and sin = opp/hyp Ay = cos(θ) x A, since Ay is (parallel to) the side adjacent to angle θ, A is the hypotenuse and cos = adj/hyp Note: Depending on the quadrant, you may have to add a – sign in front of Ax and/or Ay

Vector Addition using Trigonometry Adding Vectors - using trigonometry To add two vectors, determine the x and y component vectors for each Then add the x components together to find the x component of the vector sum And add the y components together to find the y component of the vector sum

Vector Addition using Trigonometry Adding Vectors - using trigonometry Once you have the X and Y component of the vector sum, you can use the Pythagorean Theorem to find the hypotenuse And you can use arcsin() or arccos() with one of the components to find the angle

Vector Addition using Trigonometry Vector Addition - Hyperphysics