Question 1185000
the expression is:


tan(t) * cos(t)


since tan = sin/cos, the expression bnecomes:


sin(t)/cos(t) * cos(t)


simplify to get sin(t) as your single equivalent expression.


you can use your calculator to confirm this is true.


pick any angle between 0 and 360 degrees and use the calculator to find the trigonometric function.


make sure your calculator is in degree mode and make sure you pick an angle that provides a real answer, i.e. not infinity.


i chose 300 degrees.


tan(300) * cos(300) = -.8660254030.


sin(300) = the same.


this confirms they are identical expressions.


tan function has special oconsiderations because some of the values are plus or minus infinity which is not real.


to evaluate tan(270) * cos(270), you can't do it directly.


you have to determine the equivalent expression without tan.


tan(270) * cos(270) = sin(270) / cos(270) * cos(270) = sin(270).


sin(270) = -1.


that would be your answer, after simplification.


try tan(270) * cos(270) and the calculator tells you domain error or something like that.


try sin(270)/cos(270) * cos(270) and the calculator tells you divide by 0 or something like that.


once you simplify the expression by saying sin/cos * cos = sin, then you get an answer, if that answer is possible, which, in the case of sin(270), it is.


the answer is sin(270) = -2.


bottom line - be careful with tan function and with cot function.
you may not get a real answer, which will upset our calculator.


your solution, in this problem, is tan(t) * cos(t0 = sin(t).


the rest is fyi, just in case you were trying to confirm through the use of a calculator and just happened to pick an answer that doesn't give you a real answer, such as 270 degrees, which i stumbled into.