<p>for x, an angle whose measure is between 270 and 360. cosx=5/13. Which of the following is tanx?
Answer: -5/12.
How do you do this problem????</p>
<p>Well since the angle is between 270 and 360, you know it’s in the 4th quadrant or bottom right quadrant. Being in this quadrant means that cosine is always positive, and that all of the other trig functions are negative, including tangent. So you can eliminate all the answers that are not negative.</p>
<p>Knowing that cosine is the adjacent side/ the hypotenuse, in this case, 5 is the adjacent side and 13 is the hypotenuse.
So start drawing your triangle. Your hypotenuse,13, is the longest side, so it will be diagonal. Then draw another side of the triangle, for the 5. Now draw an angle symbol between the two lines. Now finish your right triangle by drawing another line.
To find this third side, use the Pythagorean theorem. 5^2 + b^2 = 13^2 and solve for b. b is equal to 12.
So now you have your whole triangle with all of the sides. To find tangent, you do the opposite side over the adjacent side, O/A. But which side is which? To figure that out, find the angle with the symbol you drew. The side of the triangle not touching the angle is the opposite side, O, which is 12 in this case. The other leg of the triangle is the adjacent, A, in this case 5.
Since the answer must be negative since it is in the 4th quadrant and looking for tangent. TanX= O/A = -12/5.</p>
<p>Make sure you wrote down the problem correctly because -5/12 cannot be the tangent.
This would mean 5 is the O, opposite, and that 12 is the adjacent. This is contradictory to the given information of cos x= 5/13 where 5 would be A, the adjacent, and 13 is the hypotenuse. The 5 cannot be both the A and the O. So just check that your looking at the correct info.</p>
<p>-5/12 is what the princeton review answer key said…but I guess the answer key is wrong.</p>