Calculate components of a displacement vector. Vector components using trigonometry.

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We break a vector into components, finding the vector components using trigonometry.

To calculate components of a displacement vector, we project the vector onto the axes to form a right triangle, where the x component is given by the horizontal leg of the triangle and the y component is given by the vertical leg of the triangle.

To break a vector into components using SOHCAHTOA, we relate the sine function to the vertical leg (the side opposite the angle). We note that in the future we can just use hypotenuse*sin(theta) to find the opposite side in one step. Similarly, we can use hypotenuse*cos(theta) to the the adjacent side in one step, which gives us the horizontal displacement component in this case.

After finding the east and north components of displacement, we use geometric vector addition (head to tail vector addition) to add the displacement components graphically and show how the vector components add up to the original vector.

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