Trigonometric Calculations

Solve the equation sin(x) = 0.5 for 0 ≤ x ≤ 2π.

• x = π/2, 3π/2

• x = π/3, 2π/3

• x = π/6, 5π/6

• x = π/4, 3π/4

Use the double angle identity to simplify sin(2x).

• cos(2x)

• sin(x)cos(x)

• 2sin(x)

• 2sin(x)cos(x)

A ladder is leaning against a wall. If the ladder is 10 meters long and makes a 60-degree angle with the ground, how high up the wall does the ladder reach?

• 7.5 meters

• 9.2 meters

• 6.3 meters

• 8.66 meters

Evaluate cos(π/3).

• 0.5

• 2.0

• -0.5

• 1.0

Find the value of x in a triangle with sides a = 5, b = 7, and angle C = 30 degrees using the Law of Sines.

• x = 3.54

• x = 6.89

• x = 2.75

• x = 4.21

If tan(x) = -1, find the possible values of x for -π/2 ≤ x ≤ π/2.

• x = -π/2, π/2

• x = -3π/4, 5π/4

• x = -π/4, 7π/4

• x = -π/4, 3π/4

Simplify cos^2(x) - sin^2(x) using trigonometric identities.

• cos^2(x) - 1

• 1 - 2sin^2(x)

• 1 - sin^2(x)

• cos^2(x) + sin^2(x)

A Ferris wheel has a diameter of 50 meters and rotates once every 2 minutes. If you are 20 meters above the ground, write a function to model your height as a function of time.

• h(t) = 20 + 25 * sin(π * t)

• h(t) = 20 + 25 * sin(2π * t)

• h(t) = 20 + 50 * sin(π * t)

• h(t) = 20 + 25 * cos(π * t)

Calculate the value of sin(3π/4).

• 1/√2

• -1/√2

• √2

• -√2/2

In a triangle with sides a = 8, b = 10, and angle C = 60 degrees, find the length of side c using the Law of Cosines.

• Side c = 4√21

• Side c = 2√21

• Side c = 12

• Side c = 2√10