Trigonometry Core Concepts

Question 1

How many radians are in a full circle?

Accepted Answer

2π

Answer

In trigonometry, a full circle represents one complete rotation. In radian measure, this full rotation is defined as 2π radians. This is because the circumference of a unit circle (radius 1) is 2π, and radians are defined as the ratio of arc length to radius.

Question 2

In the unit circle, what are the coordinates of the point at 90∘?

Accepted Answer

(0,1)

Answer

On the unit circle, the coordinates (x, y) correspond to (cos θ, sin θ) for a given angle θ. At 90 degrees, the angle points directly along the positive y-axis. Therefore, the x-coordinate (cosine) is 0, and the y-coordinate (sine) is 1, resulting in the point (0,1).

Question 3

What is the value of 
sin(30∘)?

Accepted Answer

0.5

Answer

The sine of an angle in a right-angled triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. For a 30-degree angle, this specific ratio is 1/2. Therefore, sin(30°) equals 0.5.

Question 4

What is the tangent of 45∘?

Accepted Answer

1

Answer

The tangent of an angle is defined as the ratio of the sine of the angle to the cosine of the angle (tan θ = sin θ / cos θ). For 45 degrees, both sin(45°) and cos(45°) have a value of √2/2. Therefore, tan(45°) = (√2/2) / (√2/2) = 1.

Question 5

Convert 120∘ to radians.

Accepted Answer

2π/3

Answer

To convert degrees to radians, you multiply the degree measure by the conversion factor π/180. So, 120° * (π/180°) = 120π/180. Simplifying this fraction by dividing both numerator and denominator by 60 gives 2π/3 radians.

Trigonometry Practice Test

Trigonometry Practice Test

Trigonometry Core Concepts