SOLUTION: 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

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): You can put this solution on YOUR website!
if given and theta is in quadrant ,

answer: d.

and

answer: a.

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(52873)   (Show Source): You can put this solution on YOUR website!
.

If    = ,   then   CAN NOT   be in quadrant   IV.

The condition is   SELF-CONTRADICTORY.

The problem is a FAKE and is good for RE-CYCLING, only.

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