Question 262174
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.


<a href = "http://www.algebra.com/algebra/homework/playground/lessons/THEO-20091204.lesson" target = "_blank">http://www.algebra.com/algebra/homework/playground/lessons/THEO-20091204.lesson</a>