The measure of the angle 330 in standard position is given. Find two positive angles and two negative angles that are coterminal with the given angle.

The measure of the angle in standard position is given. Find minimal positive angle and maximal negative angles that are coterminal with the given angle.

What is the side labeled x equal to, if y = 22?

A 109 ft tree casts a shadow that is 130 ft long. What is the angle of elevation of the sun?

Find the reference angle for the angle measuring 921.

Find the reference angle for the angle measuring .

Write the following trigonometric expression in terms of sine and cosine, and then simplify.

cos x tan x

Simplify the following trigonometric expression.

tan x cos x csc x

Find the exact value of the expression.

Find the exact value of the expression.

Find the exact value of the expression.

For the function f whose graph is given, state the value of the given quantity, if it exists.

Find the exact value of the expression.

Find the exact value of the expression.

Evaluate the expression by sketching a triangle.

Evaluate the limit:

.

Evaluate the limit:

.

Find the slope of the tangent line to the graph of f at the point ( 1, 0 ).

f ( x ) = 3 + 5x – 8x ²

Find an equation of the tangent line to the curve at x = -3.

Sketch the graph of the piecewise defined function.

The graph of a function is sketched below.



Determine the interval on which the function is decreasing.

The graph shows the depth of water W in a reservoir over a one-year period, as a function of the number of days x since the beginning of the year. What was the average rate of change in W between x = 100 and x = 200?

Find the x- and y-intercepts of the rational function .

Find the horizontal and vertical asymptotes of the rational function .

The rabbit population on Mr. Jenkins' farm follows the formula: .

For this formula, t > 0 is the time in months since the beginning of the year. What is the eventual population of rabbits?

Complete the table of values (to five decimal places) and use the table to estimate the value of the limit.

x	1.9	1.99	1.999	2.001	2.01	2.1
f(x)

Complete the table of values (to five decimal places) and use the table to estimate the value of the limit.

y	–0.1	–0.01	–0.001	0.001	0.01	0.1
f(y)

Use the following graph and any other graphing device that you need to determine whether the limit exists. If the limit exists, estimate its value to two decimal places.

Given that

.

Evaluate the limit:

.

If an arrow is shot upward on the moon with a velocity of 51 m/s its height (in meters) after t seconds is given by . When will the arrow hit the moon? Round the result to the nearest thousandth if necessary.

A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the number of heartbeats after t minutes. When the data in the table are graphed, the slope of the tangent line represents the heart rate in beats per minute. Find the average heart rate (slope of the secant line) over the time interval [ 40, 42 ].

t (min)	36	38	40	42	44
Heartbeats	2,536	2,664	2,808	2,940	3,070

Find the exact value of the trigonometric function at the given real number.

Find the exact value of the trigonometric function at the given real number.

Find the limit.

A tank contains 4,000 L of pure water. Brine that contains 10 g of salt per liter of water is pumped into the tank at a rate of 25 L/min. The concentration of salt after t minutes (in grams per liter) is

.

What happens to the concentration as ?

__________ g/L

Find the degree measure of the angle with the given radian measure.

(a)      (b)

__________      __________
 

Find the exact values of the six trigonometric ratios of the angle in the triangle.Enter your answer as a fraction.



Find sec

Find the reference angle for the given angle.

210

Find the reference angle for the given angle. (If needed, type pi for in your answer)

Find the exact value for each trigonometric function.

cos 150

Find the exact value for each trigonometric function.

sin

Find the value of tan from the information given.

in quadrant II

For the function f whose graph is given, state the value of the given quantity, if it exists.



(a)    (c)

(b)    (d)

Find the limit.

Find the limit.

A ball is thrown across a playing field. Its path is given by the equation , where x is the distance the ball has traveled horizontally, and y is its height above ground level, both measured in feet.



How far has it traveled horizontally when it hits the ground? Please round your answer to the nearest tenth.

__________ ft

A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function , where the revenue R(x) is measured in dollars.

(a) What is the maximum revenue?

The downward velocity of a falling raindrop at time t is modeled by the function

.

Find the terminal velocity of the raindrop by evaluating .

A jet is flying through a wind that is blowing with a speed of 40 mi/h in the direction N 35º E. The jet has a speed of 714 mi/h in still air, and the pilot heads the jet in the direction N 50º E. Find the true speed of the jet.

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