Definitions
The inverse of the natural logarithmic function.
What is ex?
(1/4)x-3 = 4x+1
What is x = 1?
Determine the following:
1. sin(7pi/4) =
2. cos(7pi/4) =
1. sin(7pi/4) = -sqrt(2)/2
2. cos(7pi/4) = sqrt(2)/2
If theta = -21pi/4, then:
1. cot(theta) =
2. tan(theta) =
3. sec(theta) =
4. csc(theta) =
1. cot(theta) = -1
2. tan(theta) = -1
3. sec(theta) = -sqrt(2)
4. csc(theta) = sqrt(2)
Positive and negative angles in standard position that share the same terminal side.
What is a coterminal angle?
Find the exact solution for:
ln(2x-3) = 1
What is x = (e+3)/2
If theta = 13pi/3, then:
1. sin(13pi/3) =
2. cos(13pi/3) =
1. sqrt(3)/2
2. 1/2
Jose is standing 35 feet from the hospital. His angle of elevation is 41 degrees. Find the height of the hospital. Round to the nearest whole number.
How high is 30 feet?
The measure of the acute angle formed by the terminal side of the angle and the horizontal axis.
What is a reference angle?
The bacteria in a dish have an initial population of 1000, and are growing such that the population doubles every 45 minutes. Let t be the number of minutes that have passed since the initial population was measured, and let P(t) be the population at time t minutes.
Write an equation for the function P.
Use your function to determine the population of bacteria in 6 hours (360 minutes).
When will there be 250, 000 bacteria?
1. P(t) = 1000(2)t/45
2. In six hours, the bacteria will have a population of 256,000.
3. In 359 minutes, there will be 250,000 bacteria.
Given a circle of radius 5 feet formed by the central angle of 7pi/10, determine the exact arc length.
What is 7pi/2 feet?
Draw a right triangle where b = 2 and c = 3. Find:
1. sin(A) =
2. cos(A) =
3. tan(A) =
4. cot(A) =
5. sec(A) =
6. csc(A) =
1. sin(A) = sqrt(5)/3
2. cos(A) = 2/3
3. tan(A) = sqrt(5)/2
4. cot(A) = 3/2
5. sec(A) = 3(sqrt(5))/5
6. csc(A) = 2(sqrt(2))/5
When buying a new car, one consideration is how fast the car loses value, known as the depreciation rate. For example, one version of the Jeep Liberty loses value more rapidly than some of its competitors. From the initial purchase price of $23,395, an owner can expect the value of the car 5 years later to be $15, 239.
Use an exponential model to produce a function that gives the value of the Jeep in terms of the number of years, t, since the Jeep was new.
Use your model to predict the value of the Jeep when it was 3 years old.
When should the value of the Jeep decline to be $5,000?
1. J(t) = 23395(15239/233395)t/5
2. In 3 years, the Jeep's value will be $18,089.35.
3. The Jeep will have a value of $5,000 in 5 years.
You measure the angle of elevation from the ground to the top of a building that is 20 feet tall to be 53 degrees. You walk further away from the building, and you measure that the angle of elevation is 33 degrees. How far did you walk?
x = 20 tan(57 deg) - 20 tan(33 deg)