Question 1170371
tan(x) = 3/4
x = arctan(3/4) = 36.86989765 degrees in the first quadrant.
the equivalent angle in the fourth quadrant is 360 - that = 323.1301024.
tan(323.1301024) = -3/4.
that's because tangent function is positive in the first and third quadrants and negative in the second and fourth quadrants.


cos(2x) = cos(2*324.1301024) = .28
.28 * 25 = 7/25
that, i believe, is selection d.


tan(2x) = tan(2*324.1301024) = -3.428571429
that * 7 = -24/7
that, i believe, is selection f.


2*324.1301024 = 646.260202047.


equivalent angle between 0 and 360 degrees is 646.260202047 - 360 = 286.2602047 degrees.


cos(that) = .28
tan(that) = -3.428571429


if you use the trig identities, you should get the same answer.


i used them and i got the same answer.


the formulas are:


cos(2x) = cos^2(x) - sin^2(x)
tan(2x) = 2tan(x)/(1-tan^2(x))


since you said 4th quadrant, i assumed 4th quqadrant, even though you said tan(x) = 3/4 and it is actually equal to -3/4 in the fourth quadrant.


if the answers i gave you are not correct, please review the problem statement and send me a corrected.


tan is only positive in the first and third quadrant.
it is negative in the second and fourth quadrant.