Expert: Sherman D. - 1/22/2005

Question
find the values of the other 5 trignometric functions.

1) cos x = 24/25, -pi/2 < x < 0
2) cot x = -12/5, 0 < x < pi
3) csc x= -5, pi/2 < x < 3(pi)/2

Answer
I had to get a little assistance to find out how to go about doing one of the problems. For ex: i didn't know if cos^-1(x) was the same as sec or not. Well here it goes

1.)
cos(x) = 24/25, -pi/2 < x < 0
inverse cosine both sides to undo the cosine, and you get
x = ±16.2602
since you wanted it to be less than 0, then real answer is
x = -16.2602

sin(-16.2602) = (-7/25)
csc(-16.2602) = (-25/7)
sec(-16.2602) = -.0615
tan(-16.2602) = (-7/24)
cot(-16.2602) = (-24/7)

Sorry, i couldn't figure out how to put "x" and sec(x) into fraction form.

However if by -pi/2 < x < 0, you mean -(11/7) < x < 0, then the "x" value will not follow the inequality, but if by Pi, you mean 180 degrees, then it will follow the inequality.

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2.)
cot(x) = (-12/5), 0 < x < pi
tan(x) = (-5/12)
Using that
inverse tan both sides and you get
x = ±22.6199, since you wanted it to be above the 0, the real answer is x = 22.6199

sin(22.6199) = (5/13)
cos(22.6199) = (12/13)
tan(22.6199) = (5/12)
sec(22.6199) = (13/12)
csc(22.6199) = (13/5)

However if by 0 < x < pi, you mean 0 < x < (22/7), then the "x" value will not follow the inequality, but if by Pi, you mean 180 degree, then it will follow the inequality.

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3.)
csc(x) = -5, pi/2 < x < (3/2)pi
sin(x) = (-1/5)
x = ±11.5370, since you wanted it higher than pi/2

sin(11.5370) = (1/5)
cos(11.5370) = .9798
tan(11.5370) = .2041
cot(11.5370) = 4.8990
sec(11.5370) = 1.0206

I don't think this one follows the inequality.

The problems are in degree form, if you need them in radians form, just let me know and i will try and put them in radian form.