the tangent value of the angle between the x axis and the line, directed by the vector, -2j+9i,is:?

Question

a) 9/2 b)-2/9 c)2/9 d) ∞

Answer 1

r = 9 i - 2 j is a vector in 4th quadrant
tan θ = - 2 / 9
OPTION b)

Answer 2

-2/9;

j is the unit vector in the y direction, so -2 is the y component of the vector

i is the unit vector in the x direction, so 9 is the x component of the vector

The tangent of the angle with respect to the x-axis is the y-component divided by the x-component (tangent = side opposite over side adjacent).

Answer 3

First, vectors can be translated into coordinates by remembering that "i" is on the x-axis and "j" is on the y axis.

Next, the tangent of an angle (in a triangle) is the opposite over adjacent (SOH CAH TOA)

Sketch this problem as follows:
-2j+9i can be drawn as a vector between (0,0) and (9, -2)
* remember that i goes with x)

Draw a horizontal line from (0,0) to (9,0) as the bottom of the triangle. .... this side is ADJACENT to the angle (9 units long)

Draw a vertical line from (9,0) to (9, -2) to form the third side of the triangle ..... this side is OPPOSITE to the angle (and two units long)

Therefore, the tangent of the angle
tan(angle) = opposite / adjacent
= 9 /2
or = 4.5

*** ALWAYS draw a picture to help you with this sort of problem,
*** Remember, even though you are studying vectors, you are still expected to know basic trigonometry.

Good luck and have fun.

Answer 4

Z = ai + bj

tanx = b/a = - 2/9 => Answer b) - 2/9

Answer 5

Calculating the direction angle between that vector and the x axis:

alpha=arccos(9/ sqrt( 9^2+(-2^2)))
alpha=arccos(9/ sqrt( 81+4))
alpha=arccos(9/ sqrt 85)=0.2186689 (In radians)

tag(0.2186689)=0.22222222=2/9

Answer 6

b) -2/9

In general, if θ is the angle between a vector v = ai + bj and the x-axis, then v = |v| ( cos θ i + sin θ j ). I.e. a = |v| cos θ and b = |v| sin θ. Then

tan θ = sin θ/cos θ = ( b/|v| )/( a/|v| ) = b/a