Question

write the vector in the form $langle a,b
angle$.
the vector is $square$.
(simplify your answer. do not round until the final answer. then round to four decimal places as needed)

Explanation:

Step1: Find the direction angle

The direction angle \(\theta\) of the vector. Given the angle with the positive \(x -\)axis is \(155^{\circ}\), so \(\theta=180^{\circ}- 25^{\circ}=155^{\circ}\)

Step2: Use the formula for the components of a vector

The formula for the components of a vector \(\vec{v}=\langle a,b
angle\) with magnitude \(|\vec{v}| = r\) and direction angle \(\theta\) is \(a = r\cos\theta\) and \(b=r\sin\theta\). Here \(r = 4\) and \(\theta=155^{\circ}\)

• Calculate \(a\):

\(a=4\cos(155^{\circ})\)
\(\cos(155^{\circ})=\cos(180^{\circ} - 25^{\circ})=-\cos(25^{\circ})\approx - 0.9063\)
\(a = 4\times(-0.9063)=-3.6252\)

• Calculate \(b\):

\(b = 4\sin(155^{\circ})\)
\(\sin(155^{\circ})=\sin(180^{\circ}-25^{\circ})=\sin(25^{\circ})\approx0.4226\)
\(b=4\times0.4226 = 1.6904\)

Answer:

\(\langle-3.6252,1.6904
angle\)