Question

The__________ function takes as input a real number $t$that corresponds to a point$P=\left(x,y\right)$on the unit circle and outputs the $x$-coordinate.

Short answer

The cosine function takes as input a real number $t$that corresponds to a point $P=\left(x,y\right)$on the unit circle and outputs the$x-$coordinate.

Step-by-step solution

Given information

The main objective is to fill the blank with an appropriate word in the below statement:

The ______ function takes as input a real number $t$that corresponds to a point$P=\left(x,y\right)$on the unit circle and outputs the$x-$coordinate.

Explanation

For a point $P=\left(x,y\right)$on a unit circle, the cosine and sine functions with an input $t$(a real number)are defined as follows:

$\begin{array}{rcl}\cos \left(t\right)& =& x\\ \sin \left(t\right)& =& y\end{array}$

Then the cosine function has output as a $x-$coordinate.

The suitable word that fills the blank is cosine.