Question

write the vector in the form ⟨a,b⟩. the vector is ⟨□,□⟩. (round to the nearest thousandth as needed.)

Explanation:

Step1: Recall vector component formula

For a vector with magnitude \( r \) and angle \( \theta \) (in standard position), the components are \( a = r\cos\theta \) and \( b = r\sin\theta \). Here, \( r = 2 \) and \( \theta=- 50^{\circ} \).

Step2: Calculate the x - component (\( a \))

Using the formula \( a=r\cos\theta \), substitute \( r = 2 \) and \( \theta=-50^{\circ} \).
\( a = 2\cos(-50^{\circ}) \). Since \( \cos(-\alpha)=\cos\alpha \), we have \( a = 2\cos(50^{\circ})\approx2\times0.6428\approx1.286 \).

Step3: Calculate the y - component (\( b \))

Using the formula \( b = r\sin\theta \), substitute \( r = 2 \) and \( \theta=-50^{\circ} \).
\( b=2\sin(-50^{\circ}) \). Since \( \sin(-\alpha)=-\sin\alpha \), we have \( b=- 2\sin(50^{\circ})\approx-2\times0.7660\approx - 1.532 \).

Answer:

\(\langle1.286, - 1.532
angle\)