# Find the magnitude and direction angle of v=7(cos140i+sin140j. Show your work?

Apr 6, 2018

Magnitude = 7
thetha = -40 degrees, since the x component it negative it will be 40 degrees north of west

#### Explanation:

$v = 7 \left(\cos \left(140\right) i + \sin \left(140\right) j\right)$ (Use a calculator to find the sine and cosine of 140)

$v = 7 \left(- 0.766 i + 0.643 j\right)$ (Distribute 7 to the numbers in brackets)

$v = - 5.36 i + 4.50 j$ (This is the component form)

To find the magnitude, use the Pythagorean theorem

${v}^{2} = {\left(- 5.36\right)}^{2} + \left({4.50}^{2}\right)$

${v}^{2} = 28.7 + 20.3$ (Combine numbers)

${v}^{2} = 49$ (square root to get magnitude)

$\sqrt{{v}^{2}} = \sqrt{49}$

||v||=7

To find the direction, use inverse tan on the component form

$t h e t h a = {\tan}^{-} 1 \left(\frac{4.50}{-} 5.36\right)$

thetha = -40 degrees, since the x component it negative it will be 40 degrees north of west