Question 1185000: Use trigonometric identities to write the expression in terms of a single trigonometric function or a constant. tan space t space cos space t
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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