SOLUTION: Find the magnitude and direction of the vector, 0 ≤ 𝜃 < 2𝜋. 3, 5

Algebra ->  Trigonometry-basics -> SOLUTION: Find the magnitude and direction of the vector, 0 ≤ 𝜃 < 2𝜋. 3, 5       Log On


   

Question 1204900: Find the magnitude and direction of the vector,
0 ≤ 𝜃 < 2𝜋.

3, 5
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

magnitude:

direction:
direction defined as the angle theta in standard position of the terminal side through the origin and point with coordinates (a+, b)
angle theta is found by solving the trigonometric equation:
tan%28theta%29+=+b%2Fa, such that 0+%3C=+theta+%3C+2pi

Direction theta:
tan%28theta%29+=+5%2F3
theta+=tan%5E-1%28+5%2F3%29
theta=+59.04°
The terminal side of vector is in quadrant I.