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Q55.

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Precalculus Mathematics for Calculus
Found in: Page 408
Precalculus Mathematics for Calculus

Precalculus Mathematics for Calculus

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

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Short Answer

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 0.5,0.8.

See the step by step solution

Step by Step Solution

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

Starting at the point 1,0, if t0, then t is the distance along the unit circle in clockwise direction and if t<0, then t is the distance along the unit circle in clockwise direction. Here, t is a real number and this distance generates a point Px,y on the unit circle. The point Px,y 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 0.5,0.8.

Step 3. Verify the terminal point.

Note that for the given point on the unit circle cost=x and sint=y where x,y is the terminal point to real number t.

Therefore,

cos1=0.540 0.5

And,

sin1=0.841 0.8

Hence, terminal point determined by the real number t, with coordinates rounded to one decimal place 0.5,0.8.

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