MA 3972-MA-Book May 8, 2018 13:46

66 STEP 4. Review the Knowledge You Need to Score High

cos x < 0

1

2

√ 3

cos x < 0

π 0, 2π

π

(^3) π
3
π
6
π
3
π
2
3 π
2
Figure 5.3-22
Example 3
Evaluate tan−^1 (3).
Using your graphing calculator, enter tan−^1 (3). The result is 1.2490457724. Note that the
range of tan−^1 xis (−π/2, π/2) and−π/2≤ 1. 2490457724 ≤π/2. Thus tan−^1 (3) ≈
1 .2490457724.
Example 4
Evaluate sin
(
cos−^1
(√
3
2
))
.
Note that cos−^1
(√
3
2
)

π
6
, and thus, sin
(
π
6
)
= 0 .5. Or you could use a calculator and
enter sin
(
cos−^1
(√
3
2
))
and get 0.5.
Exponential and Logarithmic Functions
Exponential function with basea:f(x)=axwherea>0 anda =1.
Domain:{all real numbers}. Range:{y|y> 0 }.y-Intercept: (0, 1). Horizontal asymptote:
x-axis. Behavior: strictly increasing. (See Figure 5.3-23.)
00
(0, 1) (0, 1)
y = ax, a > 1
y = ax, 0 < ay < 1
x x
y
y
Figure 5.3-23