SOLUTION: find cos theta if cot theta is 4/3?

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Question 1102586: find cos theta if cot theta is 4/3?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
cot%28theta%29=4%2F3
Because cot%28theta%29=4%2F3 and tan%28theta%29=1%2Fcot%28theta%29=3%2F4 are positive,
the angle theta is in quadrant I
(an acute angle, or an angle coterminal with an acute angle),
or in quadrant III.
If theta must be an acute angle,
a tangent trigonometric ratio of 3%2F4
corresponds to an acute angle theta in a right triangle
with (opposite side)/(adjacent side)=3/4.
A right triangle with leg lengths 3 and 4,
has a hypotenuse of length sqrt%283%5E2%2B4%5E2%29=sqrt%289%2B16%29=sqrt%2825%29=5 .
With an opposite leg length of 3 ,
and a hypotenuse leg length of 5,
the highlight%28cos%28theta%29=3%2F5=0.6%29 .
That corresponds to theta=approximately36.87%5Eo
(or theta=approximately0.6435 in radians).

If theta was an angle in quadrant III, such as theta=approximately216.87%5Eo ,
then it would be cos%28theta%29=-0.6 .