Worksheet 1

Worksheet 1 Key

1. Factor (into linear factors)

(a) (b)

Ans: (x- 6)(x- 1) Ans: (x- 5)(x+5)

Ans: (3x- 1)(2x+1) Ans: (x)(3x- 1)(x+1)

2. Simplify as much as possible

(a) (b)

Ans:

3. Let

. Find the following (and simplify your answer as much as possible).

(a)

Ans:

(b)

Ans:

(c)

Ans:

(d)

Ans:

(e)

Ans:

(g)

Ans: Use parts (f) and (d) to get

(h)

Ans: Use part (g) to get

(i)

Ans:

4. Find exact values. (You may use a chart for this for now, but be forewarned that on the quizzes and exams you will have to know the trigonometric values of the standard angles by memory.)

(a)

Ans:

(b)

Ans:

(c)

Ans:

(d)

Ans: -1 (e)

(f)

(g)

Ans: Ans: Ans:

5. Estimate the following (use your calculator only to check your estimate)

(a)

Ans: Since is between and, but is closer to , a rough estimate is

(b)

Ans: Since 185° is between 180° and 210° , but is closer to 180° , a rough estimate is cos 185° » - 0.95

(c)

Ans: Since 3 is between and p , but is closer to p , a rough estimate is cos 3 » - 0.95

(d)

Ans: Since 1° is only very slightly larger that 0° , we estimate sin 1° » 0.01

6. Complete each right triangle

(a)

Ans: Using either the Pythagorean Theorem or the similarity with the 3-4-5 right triangle, you find that the hypotenuse is 20 units long.

(b)

Ans: Using either the Pythagorean Theorem or the fact that this is a 5-12-13 right triangle, you find that the unlabeled leg is 12 units long.

(c)

Ans:

7. Solve each inequality for x. You may give your solution using either inequality notation, interval notation, or by graphing on a number line.

(a) (b)

Ans: Ans: