SOLUTION: Use trigonometric identities to write the expression in terms of a single trigonometric function or a constant. tan space t space cos space t

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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