Mastering Trigonometry Concepts

What is the sine of a 30-degree angle?

• 0.5

• 0.75

• 1.0

• 0.25

Define the cosine function in terms of a right triangle.

• cos(theta) = hypotenuse/adjacent

• cos(theta) = adjacent/opposite

• cos(theta) = opposite/hypotenuse

• cos(theta) = adjacent/hypotenuse

What is the value of tan(45 degrees)?

• 2

• 1.5

• 0

• 1

If sin(x) = 0.5, what are the possible values of x?

• x = 45° + 360°k

• x = 90° + 360°k

• x = 120° + 360°k

• x = 30° + 360°k, x = 150° + 360°k (k ∈ ℤ)

Explain the Pythagorean identity in trigonometry.

• sin(θ) + cos(θ) = 0

• tan²(θ) + cot²(θ) = 1

• sin²(θ) + cos²(θ) = 1

• sin²(θ) - cos²(θ) = 1

Calculate the length of the opposite side if the hypotenuse is 10 and the angle is 30 degrees.

• 3

• 7

• 8

• 5

What is the relationship between the angles in a right triangle?

• The two non-right angles are always equal.

• The right angle measures 60 degrees.

• The sum of the two non-right angles is 90 degrees.

• The sum of all three angles is 180 degrees.

How do you convert degrees to radians?

• radians = degrees × (180/π)

• radians = degrees + 180

• radians = degrees × (π/180)

• radians = degrees ÷ 180

What is the value of cos(60 degrees)?

• 0

• 0.5

• 1

• -0.5

Describe the unit circle and its significance in trigonometry.

• The unit circle is a circle of radius one centered at the origin, crucial for defining trigonometric functions.

• The unit circle is used to define logarithmic functions.

• The unit circle is a square with a radius of one.

• The unit circle is a circle of radius two centered at the origin.