Date: Mar 13, 2013 10:37 AM
Author: Peter Scales
Subject: Re: ACT Math Question

> I am having some difficulty with the following ACT
> practice problem:
> For X, an angle whose measure is between 270° and
> 360°, cosX=5/13. Which of the following equals tanX?
> A. -5/12
> B. -5/13
> C. 5/13
> D. 5/12
> E. 12/13
> The book I am using provides the answer and an
> explanation, but the explanation uses process of
> elimination to find the answer without actually
> describing a method of solving the problem. I would
> like to understand how to actually find the answer.
> Can someone lend a helping hand?
> Thanks!

Hi Christopher,

I don't know what ACT is, but this is absolutely elementary trig, which you must understand if you want to do anything at all in trig.

Draw coord axes yox and a circle of radius r (always +ve)centred at the origin.
Angles are measured anticlockwise from ox. The quadrants are called 1, 2, 3, 4 (or I, II, III, IV).
For an arbitrary position of the radius vector, project it onto the x-axis to give a segment X long. The join from the outer end of X to the outer end of r is Y long.
The sign of X and Y come from the coord axes.
In quadrant 1 all trig functions are +ve.
In quadrant 2 sin is +ve.
In quadrant 3 tan is +ve.
In quadrant 4 cos is +ve.

For the example you give with 270 < theta < 360, r lies in the 4th quadrant, and r=+13, X=+5 since cos(theta)=5/13
By pythagoras Y = -12
.: tan(theta) = Y/X = -12/5
so the answer is none of those given!

Also cos(theta)=5/12
.: theta = + or - 67.38deg or 292.62deg

tan(67.38) = 12/5 = 2.4

tan(-67.38) = -12/5 = -2.4

tan(292.62) = -12/5 = -2.4

I hope this helps.
Please feel free to ask more questions if you need more help.

Regards, Peter Scales.