SOLUTION: I have this problem and need the solution and an explanation for it: 0�<=[theta]<360�+cot[theta]=-1.4176[theta]=x {{{0�<=[theta]<360�+cot[theta]=-1.4176[theta]=x}}} {problem

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Question 262174: I have this problem and need the solution and an explanation for it:
0�<=[theta]<360�+cot[theta]=-1.4176[theta]=x
{problem in brackets}
The written form was this:
"If 0deg <= [theta] <360deg and cot[theta] = -1.4176 then determine [theta] to the nearest tenth".
Thank you, Steven

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
working from the written statement, I get this:

"If 0deg <= [theta] <360deg and cot[theta] = -1.4176 then determine [theta] to the nearest tenth".

what they are saying is that the angle is between 0 and 360 degrees.

they are also saying that tangent of the angle = -1.4176.

if you find the angle whose tangent is -1.4176, then you have found the angle they are looking for.

using your scientific calculator, you find the arctangent of -1.4176.

on my calculator that equals -54.8001834 degrees.

that would be in the 4th quadrant.

to find the equivalent positive angle, you add 360 to it to get:

angle equals 305.1998166 degrees.

put that angle in your calculator and get the tangent of it.

you get:

tangent of 305.1998166 degrees = -1.4176.

since that's where we started from, you're good.

basically you had 2 requirements.

you needed to find the angle whose cotangent was equal to -1.4176.

you needed to find the equivalent angle that was between 0 and 360 degrees.

any angle plus or minus 360 degrees is equivalent to the same angle.

0 is equivalent to 360 is equivalent to 720, etc.

if the angles are equivalent, then their trigonometric functions are also equivalent.

tan(-55) = tan(-55 + 360) = tan(305).

here's a tutorial you may be interested in to understand this better.

http://www.algebra.com/algebra/homework/playground/lessons/THEO-20091204.lesson