Question

What is the value of cosθ given that (−2, −3) is a point on the terminal side of θ ?

Answer 1

Answer:

-0.555

Step-by-step explanation:

The terminal point of the vector in this problem is

(-2,-3)

So, it is in the 3rd quadrant.

We want to find the angle $\theta$ that gives the direction of this vector.

We can write the components of the vector along the x- and y- direction as:

$v_x = -2\\v_y = -3$

The tangent of the angle will be equal to the ratio between the y-component and the x-component, so:

$tan \theta = \frac{v_y}{v_x}=\frac{-3}{-2}=1.5\\\theta=tan^{-1}(1.5)=56.3^{\circ}$

However, since we are in the 3rd quadrant, the actual angle is:

$\theta=180^{\circ} + 56.3^{\circ} = 236.3^{\circ}$

So now we can find the cosine of the angle, which will be negative:

$cos \theta = cos(236.3^{\circ})=-0.555$