Question

An angle, θ, is in standard position. The terminal side of the angle passes through the point (-5, -3). Find tanθ.

Answer 1

If the terminal ray of an angle passes through (-5, -3), that means it passes through x coordinate -5 and y coordinate -3.  Both x and y are negative in only one quadrant and that is the third one.  If we plot the point (-5, -3) in the coordinate plane in Q3, and then draw a vertical line to connect that point to the negative x axis and then draw a line to connect that point to the origin, what we have created is right triangle with a base of -5 and a height of -3. The tangent ratio relates the side opposite the reference angle to the side adjacent to the reference angle.  We have both of those measures already and do not have a need for the length of the hypotenuse since the tangent ratio doesn't use it.  The tangent of the reference angle is -3/-5 which is 3/5.

Answer 2

Answer:

$\tan \theta = 0.6$

Step-by-step explanation:

The point is located at the 3rd Quadrant of the Cartesian plane, which means that θ is between 180° and 270°. The value of the trigonometric function is:

$\tan \theta = \frac{y}{x} = \left(\frac{-3}{-5}\right)$

$\tan \theta = 0.6$