Pre calculus magnitudes and vectors

Question

Write the vector with magnitude 7 and direction 300° in rectangular form

Answer 1

||v||< (cosθ), sinθ) >. ||v|| = magnitude = 7 and θ = 300º

so, < 7(cos300°), 7(sin300°) >. 300º is 60º reference angle in the 4th quadrant so cosine of 60º is +1/2 and the sine of 60º is -√3 /2

< 7(1/2), 7(-√3 /2) >

<3.5, -6.06>