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Found in: Page 408

### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

# The unit circle is graphed in the figure below. Use the figure to find the terminal point determined by the real number $t$, with coordinates rounded to one decimal place.$t=1$

The terminal point determined by the real number $t$, with coordinates rounded to one decimal place $\left(0.5,0.8\right)$.

See the step by step solution

## Step 1. State the definition of the terminal point on the unit circle.

Starting at the point $\left(1,0\right)$, if $t\ge 0$, then $t$ is the distance along the unit circle in clockwise direction and if $t<0$, then $\left|t\right|$ is the distance along the unit circle in clockwise direction. Here, $t$ is a real number and this distance generates a point $P\left(x,y\right)$ on the unit circle. The point $P\left(x,y\right)$ obtained in this way is called the terminal point determined by the real number $t$.

## Step 2. Use the figure to find the terminal point determined by the real number t.

Draw the coordinate corresponding to $t=1$.

Since given point on circle lies in the first quadrant, therefore both $x$-axis and $y$-axis are positive and can be approximated to $\left(0.5,0.8\right)$.

## Step 3. Verify the terminal point.

Note that for the given point on the unit circle $\mathrm{cos}t=x$ and $\mathrm{sin}t=y$ where $\left(x,y\right)$ is the terminal point to real number $t$.

Therefore,

$\begin{array}{c}\mathrm{cos}\left(1\right)=0.540\\ \approx 0.5\end{array}$

And,

$\begin{array}{c}\mathrm{sin}\left(1\right)=0.841\\ \approx 0.8\end{array}$

Hence, terminal point determined by the real number $t$, with coordinates rounded to one decimal place $\left(0.5,0.8\right)$.