Find the component form of v given its magnitude and the angle it makes with the positive x-axis. Round your answer to four decimals.‖v‖=9,θ=150°
Question
Find the component form of v given its magnitude and the angle it makes with the positive x-axis. Round your answer to four decimals.
‖v‖ = 9,
θ = 150°
Solution
To find the component form of vector v, we can use the formulas:
v_x = ‖v‖ * cos(θ) v_y = ‖v‖ * sin(θ)
Given that ‖v‖ = 9 and θ = 150°, we first need to convert the angle from degrees to radians because the trigonometric functions in most programming languages use radians, not degrees.
1 radian = 180/π degrees So, 150 degrees = 150 * π/180 radians = 5π/6 radians
Now we can substitute ‖v‖ and θ into the formulas:
v_x = 9 * cos(5π/6) = -7.7942 v_y = 9 * sin(5π/6) = 4.5000
So, the component form of vector v is (-7.7942, 4.5000).
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