Question

a vector has an x - component of length 3.5 and a y - component of length 3. what is the angle of the vector? (hint: use the inverse tangent.)
a. 67.2°
b. 31.0°
c. 40.6°
d. 59.0°

Explanation:

Step1: Recall the formula for the angle of a vector

The formula for the angle \(\theta\) of a vector with \(x -\)component \(A_x\) and \(y -\)component \(A_y\) is \(\theta=\tan^{- 1}(\frac{A_y}{A_x})\). Here, \(A_x = 3.5\) and \(A_y=3\).

Step2: Substitute the values into the formula

\(\theta=\tan^{-1}(\frac{3}{3.5})\).
First, calculate \(\frac{3}{3.5}=\frac{30}{35}=\frac{6}{7}\approx0.857\).
Then, \(\theta=\tan^{-1}(0.857)\).
Using a calculator, \(\tan^{-1}(0.857)\approx40.6^{\circ}\).

Answer:

C. \(40.6^{\circ}\)