Review the following concepts if needed:

- Cartesian Coordinates Help
- Circles in the Plane Help
- Primary Circular Functions Help
- Secondary Circular Functions Help

**The Circle Model Practice Test**

A good score is eight correct.

1. A relation has the equation *x* ^{2} + *y* ^{2} = 16. The graph of this relation, in Cartesian coordinates, looks like

(a) a straight line

(b) a parabola

(c) a spiral

(d) a circle

2. The value of tan 90° is

(a) 0

(b) 1

(c) π

(d) not defined

3. Which of the following statements is true?

(a) tan *θ* = 1/cot *θ* , provided cot *θ* ≠ 0

(b) tan *θ* = 1 – cos *θ* , provided cos *θ* ≠ 0

(c) tan *θ* = 1 + sin *θ* , provided sin *θ* ≠ 0

(d) tan *θ* + cot *θ* = 0, provided cot *θ* ≠ 0 and tan *θ* ≠ 0

4. With regard to the circular functions, an angle of 5π rad can be considered the same as an angle of

(a) 0°

(b) 90°

(c) 180°

(d) 270°

5. An ordinate is

(a) the value of a dependent variable

(b) the value of an independent variable

(c) a relation

(d) a function

6. The sine of 0° is the same as the sine of

(a) 45°

(b) 90°

(c) 180°

(d) 270°

7. Suppose the tangent of a certain angle is –1.0000, and its cosine is –0.7071, approximated to four decimal places. The sine of this angle, approximated to four decimal places, is

(a) 1.0000

(b) 0.7071

(c) –0.7071

(d) 0.0000

8. What is the approximate measure of the angle described in Question 7?

(a) 0°

(b) 90°

(c) 180°

(d) None of the above

9. Set your scientific calculator, or the calculator program in your computer, to indicate radians. Activate the inverse-function key (in Windows, put a checkmark in the box labeled “Inv”). Be sure the calculator is set to work with decimal numbers (in Windows, put a dot or a check in the space labeled “Dec”). Next, find the difference 1 – 2 using a calculator, so it displays –1. Then hit the “cos” function key, thereby finding the measure of the angle, in radians, whose cosine is equal to –1. The resulting number on the display is an excellent approximation of

(a) *π/2*

(b) *π*

(c) 3π/2

(d) *2π*

10. Use your scientific calculator, or the calculator program in your computer, to find the cosine of *1.6π* rad (that is, *8π/5* rad). Rounding the answer to two decimal places, you should get

(a) an error or an extremely large number

(b) 0.95

(c) –0.31

(d) 0.31

**Answers:**

1. d

2. d

3. a

4. c

5. a

6. d

7. a

8. d

9. c

10. d

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