Question 1170371: if tanθ=3/4 and θ is in quadrant IV,cos2θ= ? and tan2θ= ?
options for first ?
a. 33/25
b. -17/25
c. 32/25
d. 7/25
e. 24/25
options for second ?
a. 24/7
b.-24/7
c. 7/25
d.-7/25
e. 13/7
f.-13/7
Found 3 solutions by MathLover1, Theo, ikleyn:
Answer by MathLover1(20850)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! 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.
Answer by ikleyn(52871)  (Show Source):
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