Exponential & Logarithmic Functions
The inverse of ln x
What is e^x ?
Convert to radians: 240 degrees
What is 4pi/3 ?
If sinx = 4/5, what is cos(90 - x)?
What is 4/5?
Which trigonometric function is positive in the 3rd quadrant?
What is tangent (or cotangent)?
In how many ways can 1st, 2nd, and 3rd place be awarded to 10 competitors?
What is the 720?
Solve for x: 2^(x+5) = 64
What is x = 1?
Solution:
2^(x+5) = 2^6
x+5 = 6
x = 1
Find the arc length formed by a central angle of 30 degrees in a circle with a radius of 6 cm.
What is pi cm? (Or what is 3.14 cm?)
Solution:
s = r(theta)
s= (6 cm) (30 deg)(pi rad/ 180 deg)
s = (6 cm)(pi/6)
s = pi cm
The angle of depression from the top of a tower to a grounded airplane is 19o. If the tower is 325 feet tall, how far is the plane from the base of the tower?
What is 943.87 feet?
Convert to rectangular form: r = 4sec(theta)
What is y = 4?
What is 9/13?
Solve for x: log(3x+7) = 2
What is x = 31?
Solution:
3x+7 = 100
x = 31
Find an angle that is coterminal to 3pi/17
What is 37pi/17? (or -31pi/17)
Solution:
Add 2pi: 3pi/17 + 34pi/17 = 37pi/17
Subtract 2pi: 3pi/17 - 34pi/17 = -31pi/17
Solve for a: tan 22 = a/300
(the angle is in degrees)
What is 121.21 ?
What are the equations of the asymptotes of the graph y = tan x ?
What is pi/2 +/- pi?
What is the 3rd term in the expansion of (2x + y)5?
What is 80x3y2?
Solve for x: e^(2x) - 4e^x + 3 = 0
What is x = {0, ln3} ?
Solution:
((e^x) - 3)((e^x) - 1) = 0
e^x = 3 OR e^x = 1
x = ln3 OR x = ln1
{0, ln3}
Sin-1(sin(7pi/6))
What is -pi/6?
Find the length of the hypotenuse of right triangle ABC, if angle A = 37, angle B = 90 and side c = 10.
What is 12.52 ?
Solution:
cos 37 = 10/hypotenuse
hypotenuse = 10/cos 37
hypotenuse = 12.52
What is the polar form of the rectangular coordinate (-4, 7)?
What is (sqrt(65), 119.74o) ?
The letters of the word RANDOM are arranged randomly. What is the probability that an arrangement chosen at random ends with a vowel?
What is 1/3?
In 2000, the population of Israel was 5 million. By 2050, the population is expected to grow to 10 million. Use the exponential growth model A = Aoe^kt, where t is the number of years after 2000, to model this population growth.
What is A = 5e^0.0139t ?
Solution:
10 = 5e^50k
2 = e^50k
ln2 = 50k
k = (ln2)/50 = 0.0139
Find the sin t if the cos t = sqrt(21)/5
What is 2/5?
Solution:
(sin t)^2 + (sqrt(21)/5)^2 = 1
(sin t)^2 = 1 - (21/25)
(sin t)^2 = 4/25
sin t = 2/5
What is the angle of elevation of the sun if a 125ft tower casts a 172ft shadow?
What is 36 degrees?
Solution
tan (theta) = 125/172
theta = (tan^-1)(0.7267)
theta = 36 degrees
cos((sin^-1)(9/41))
What is 40/41 ?
What is 0.307?