1. 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:

2. 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.

3. 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

4. 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

5. 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

6. 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

7. Vector Addition using Trigonometry
Vector Addition - Hyperphysics