Lesson 6.1.1

6-1. See below:
a. Since graphs intersect at more than one point, there must be more than
one solution to the equation.
b. There are 2 solutions. From the graph we can see
that x =
and
.
c. It shows where the y-coordinate or sin x =
d. x =
or
.
; Students may use a unit circle or the graph.

6-2. Draw a vertical line at x =

6-3. A horizontal line drawn at y = 2 does not intersect the unit circle. The value 2
is not in the range for y = sin x.

6-4. Answers vary.

6-5. See below:
.
x=
. x=
,
a. x =
,
b. x =
,
c. x =

.
,
6-6. See below:
All real numbers.
a. −1 < y < 1
b. 2π

6-7. See below:
. 2 solutions: 0 and π.
a. infinitely many
b. An integer multiple of 2π, because it’s the period.

6-8. See below:
. An infinite number of them. We can see 12 on the graph below.
a.
x=
b. Add 2πn to
c.
d.
,
, n is any integer.

6-9. See below:
. The y-coordinates of the points are
.
a. We can continue to go around the circle infinitely many times. Each time
around is an angle of 2π.

The selected answers provide a reference to the lesson in which the topic was covered.
Problems designated as (AR) are Alegbra Review, (GR) are Geometry Review, and
(EP) are Extra Practice. You can find Extra Practice at www.cpm.org.

6-10. See below:
a.
b.

,
+ 2πn,
+ 2πn
6-11. (6.1.1) See below:
. Since the string is 30 inches in length, the maximum point will be 30 inches above the
minimum.
a. 15
b. 20
c.
d. negative cosine
e. h = −15cos

6-12. (4.2.1) See below:
a. 2
b. undefined
c. −
d.

6-13. (2.3.2) See below:
a. 7 +
+5
+ 20
b.

6-14. (AR)


6-15. (GR, SB-9) 25.6 feet

6-16. (5.1.1) See below:
. 0.8 liters/hr
a. 0.504 liters/hr

6-17. (1.1.3) g(−1) = 3, g(3) = 3, g(a) = a2 − 2a, g(t − 2) = t2 − 6t + 8

6-18. (AR, SB-13) See below:
.
a. 1 ±