Trigonometric Difference Identities Answers

Given: < A < and < B < What is tan(A – B)?

The merry-go-round at the fair rotates 12 times each minute, and children are 15 feet from the center of the wheel when they are in their seats. What is the linear velocity of the children in feet per hour?

Review the steps of the proof.Step 1: Step 2: Step 3: Step 4:

What is the period of the function ?

Review the proof of sin(A – B) = sinAcosB – cosAsinBsin(A – B) = Step 1: Step 2: Step 3: Step 4: = sinAcosB – cosAsinB

Which expression is equivalent to 30°?

Which values are two of the possible solutions to the equation?

What is the equation of the graph below?

What is the value of cos(15°)?

Which expression is equivalent to ?

Which transformation should be applied to the graph of the function to obtain the graph of the function ?

Review the steps of the proof of the identity .Step 1: = Step 2: = Step 3: = Step 4: = Step 5:

How many degrees is radians?

Which values represent solutions to , where x [0, 2)?

What is the exact value of ?

Which functions are symmetric with respect to the origin?

Review the proof of the identity cos(π − A) = −cosA.cos(π − A)Step 1: = cosπcosA − sinAsinπStep 2: = (−1)(cosA) + (sinA)(0)Step 3: = −1cosA + (sinA)(0)Step 4: = −cosA + 0Step 5: = −cosA

Given: cos(3x – 180°) = , where 0 ≤ x < 180°Which values represent the solutions to the equation?

Suppose tan(b) = –2, and the terminal side of b is located in quadrant II. What is cot(b)?

Which expression is equivalent to cos(40°)cos(10°) + sin(40°)sin(10°)?

Which of the following is the equation of the function below?

What is the value of sin(80°)cos(20°) – cos(80°)sin(20°)?

When simplified, is equivalent to which expression?

During high tide around 11:00 p.m., the water level is 3 feet above a marker on a pier. The following day, during low tide around 5:12 a.m., the water level has dropped 3 feet below the marker. The height of the water is modeled by the function , where x is the time in hours since 11:00 p.m.What is the height of the water at 2:15 a.m.?

The function g(x) represents f(x) = after translating units left and 4 units up.Which equation represents g(x)?

Suppose the function h(x) = sinx is translated units left and 11 units down. Which graph represents the result?

Review the graph.

Which is an x-intercept of the graph of the function ?

A particle travels in a circle around a fixed point at 16 revolutions per minute. The linear velocity of the particle is 240π inches per minute.What is the distance, in inches, between the particle and the fixed point?

The table shows the temperatures in degrees Celsius, y, inside a shed at x hours past noon. The maximum and minimum temperatures are shown.

At a certain location, the number of hours of sunlight is modeled by y = where x represents the number of weeks after the summer solstice.Based on the model, what is the minimum number of hours of sunlight at this location?

A seat on a Ferris wheel is level with the center of the wheel. The diameter of the wheel is 200 feet. Suppose the wheel rotates 60°, causing the height of the seat to decrease. How much closer to the ground is the seat after the rotation?

Suppose you want to transform the graph of the function into the graph of the function . Which transformations should you perform?

Over which interval is the graph of y = cos(x) strictly increasing?

In which quadrant(s) is csc(x) positive?

How does the graph of y = sec(x + 3) – 7 compare with the graph of y = sec(x)?

Consider the function y = cos(x). Which change would increase the period by a factor of 3?

Let a function y represent the water level in a harbor measured in meters, and let x represent the number of hours since high tide. At time x = 0, the water level is 19.5 meters (a maximum). At time x = 6.26 hours, the water level is 10.5 meters (a minimum). The period of the function is 12.5 hours.After how many hours is the water expected to reach a depth of 17 meters for the first time? Round to the nearest tenth of an hour.