SOLUTION: Given cos 6 theta = 4/5, P(6 theta) belongs to Q1, tan (6 theta) is equal to a) 3/4 b) 4/3 c) - 3/4 d) - 4/3

Algebra ->  Trigonometry-basics -> SOLUTION: Given cos 6 theta = 4/5, P(6 theta) belongs to Q1, tan (6 theta) is equal to a) 3/4 b) 4/3 c) - 3/4 d) - 4/3      Log On


   

Question 824914: Given cos 6 theta = 4/5, P(6 theta) belongs to Q1, tan (6 theta) is equal to
a) 3/4
b) 4/3
c) - 3/4
d) - 4/3
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
All angles in quadrant 1 are acute angles, and all acute angles are in quadrant 1.
In the right triangle below, the acute angle 6theta has
cos%286theta%29= (adjacent side)/(hypotenuse) =4%2F5



According to the Pythagorean theorem,
4%5E2%2Bx%5E2=5%5E2
16%2Bx%5E2=25
x%5E2=25-16
x%5E2=9
x=3
So tan%286theta%29= (opposite side)(adjacent side) =highlight%283%2F4%29