Question

find the magnitudes of the horizontal and vertical components for the vector v, if α is the direction angle of v from the horizontal.
α = 269.3°, ||v|| = 580
the magnitude of the horizontal component of v is
(round to the nearest integer as needed.)

Explanation:

Step1: Identify horizontal component formula

The horizontal component $v_x$ of a vector is $|v|\cos\alpha$.

Step2: Substitute values into formula

$v_x = 580 \times \cos(269.3^\circ)$

Step3: Calculate cosine value

$\cos(269.3^\circ) \approx \cos(270^\circ - 0.7^\circ) \approx -\sin(0.7^\circ) \approx -0.012217$

Step4: Compute horizontal component

$v_x \approx 580 \times (-0.012217) \approx -7.08586$

Step5: Round to nearest integer

$-7.08586 \approx -7$

Answer:

-7