Expert: Ahmed Salami - 10/30/2004

Question
I don't understand what you did here.Please explain.cot # = 2 implies
tan # = 1/2
# = arc tan (1/2)

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Followup To
Question -
Can you please explain what is wrong with my way of doing the following problem:If theta is an angle in quadrant 1 and cot^2theta - 4=0, what is the value of theta to the nearest degree?The answer is 27, but that's not what I got.Please explain why my way is wrong even though it seems logical to do. Thank you. Here is my work:(after all trig functions there is a theta even though I didn't write it)
cot^2=4
sqrt both sides
cot=2
substitute cos/sin for cotangent then I substituted 1-cos for sin.So I got:
[cos/(1-cos)]=2
Then I cross-multiplied
cos=2(1-cos)
cos=2-2cos
Then I added 2cos to both sides getting:
3cos=2
costheta=2/3
theta=48.1896
rounded to
theta=48


Answer -
Hi Jeff,
I can see one mistake.
cot = cos/sin
but sin = sqrt(1 - cos^2)
and not 1 - cos like you wrote. Try looking into that.
But you could simply have said
cot # = 2 implies
tan # = 1/2
# = arc tan (1/2)
which is easier.
Let me know how far you go with it.
Regards.

Answer
Hi Jeff,
The cotangent of any angle is the reciprocal of the tangent of the angle i.e
cot # = 1/tan #
So if cot # = 2, tan # = 1/2
I hope you now get it. It gives the correct answer, doesn't it? I hope you also tried the other way i told you.
Regards.