AP Practice - Trigonometry

Match the following. Assume θ is an angle in standard position.

• Displacement of θ from x-axis

• tan⁡θ

• Slope of the terminal side θ

• cos⁡θ

• Displacement of θ from y-axis

• sin⁡θ

Let 𝜃 be the angle in standard position such that OP is the terminal ray. What is sin⁡𝜃?

• sin𝜃 = 4

• sin𝜃 = 4/5

• sin𝜃 = 3

• sin𝜃 = 3/5

Which graph would have a frequency of 2 and a maximum value of −4?

• 𝑓(𝑥) = 3 cos⁡(4𝜋𝑥)+7

• 𝑎(𝑥) = 3 cos⁡(1/4𝜋𝑥)−7

• 𝑔(𝑥)=3 cos⁡( 4𝜋𝑥)−7

• 𝑎(𝑥)=3 cos⁡(1/4𝜋 𝑥)+7

Let there be an angle 𝜑 such that 𝜋/2 < 𝜑 < 𝜃.

Which statement is true?

• sinφ < sinθ

• cosθ < cosφ

• tanφ < tanθ

• sinφ > sinθ

Which graph is equivalent to y = sinx?

• f(x) = cos(x + π)

• g(x) = cos(x − π)

• h(x) = cos(x + π/2)

• j(x) = cos(x - π/2)

Which statement is true about the graph of h(x) = sin x on the interval 0 < x < π/2?

• h(x) is increasing at an increasing rate.

• h(x) is increasing at a decreasing rate.

• h(x) is decreasing at an increasing rate.

• h(x) is decreasing at a decreasing rate.

Which statement is true about the coordinate point P: (-2√3, 2) located on a terminal ray for an angle in standard position θ intersecting a circle centered at the origin?

• The point P is intersecting the unit circle and the x and y coordinates are equal to cosθ and sinθ respectively.

• The point P is intersecting a circle with a radius of 4 and the x and y coordinates are equal to cosθ and sinθ respectively.

• The point P is intersecting the unit circle and the values of cosθ and sinθ can be found by dividing the x and y coordinates respectively by the radius.

• The point P is intersecting a circle with a radius of 4 and the values of cosθ and sinθ can be found by dividing the x and y coordinates respectively by the radius.

For which interval in 0 < θ < 2π are the values of sin 0 and cos 0 both increasing?

• 0 < θ < π/2

• π/2 < θ < π

• π < θ < 3π/2

• 3π/2 < θ < 2π

Which best describes the function shown in the graph?

• The function can measure the vertical displacement from the x-axis on the unit circle as angle moves in a counterclockwise direction.

• The function can measure the horizontal displacement from the x-axis on the unit circle as angle moves in a counterclockwise direction.

• The function can measure the vertical displacement from the y-axis on the unit circle as angle moves in a counterclockwise direction.

• The function can measure the horizontal displacement from the y-axis on the unit circle as angle moves in a counterclockwise direction.

A physical therapy center has a bicycle that patients use for exercise. The height, in inches (in), of the bicycle pedal above level ground periodically increases and decreases when used. The figure gives the position of the pedal P at a height of 12 inches above the ground at time t=0 seconds. The pedal's 8-inch arm defines the circular motion of the pedal. If a patient pedals 1 revolution per second, which of the following could be an expression for h(t), the height, in inches, of the bicycle pedal above level ground at time t seconds?

• 8 - 12sint

• 12 - 8sint

• 8 - 12 sin(2πt)

• 12 - 8 sin(2πt)