Trigonometry and Unit Circle Concepts Quiz

Challenge yourself with 17 questions on trigonometry covering sine, cosine, tangent, unit circle, identities, and more.

Practice Learn Test

What is the value of sin(90°)?

-1

0.5

If the angle θ in the unit circle corresponds to a point (x, y) on the circle, what is cos(θ)?

1/x

1/y

What is the value of sin(θ) when θ = 270°?

-1

0.5

What is the exact value of cos(45°)?

√2/2

√3/2

1/2

What is the period of the function sin(θ)?

2π

π/2

4π

What is the range of the sine function for real numbers θ?

-1 ≤ sin(θ) ≤ 1

0 ≤ sin(θ) ≤ 1

-∞ < sin(θ) < ∞

1 ≤ sin(θ) ≤ -1

Which of the following is an identity for tan(θ) in terms of sine and cosine?

tan(θ) = cos(θ)/sin(θ)

tan(θ) = sin(θ)/cos(θ)

tan(θ) = 1/cos(θ)

tan(θ) = 1/sin(θ)

What is the value of cos(θ) when θ = 120°?

1/2

-1/2

√3/2

-√3/2

Which of the following represents the Pythagorean identity?

sin^2(θ) + cos^2(θ) = 1

tan^2(θ) + 1 = sec^2(θ)

1 + cot^2(θ) = csc^2(θ)

All of the above

#10

For an angle θ in the unit circle, if cos(θ) = -√3/2, what quadrant is θ in?

III

#11

If tan(θ) = 1, what is the smallest positive angle θ in degrees?

45°

90°

135°

180°

#12

Which of the following angles corresponds to the same terminal side as 330° in the unit circle?

-30°

30°

-60°

390°

#13

Given the angle θ in the unit circle produces a point (x, y), which of the following represents the arc length of the circle segment corresponding to angle θ in radians?

θ/2π

#14

For angle θ in the unit circle, if the angle is 3π/4 radians, what are the sine and cosine values?

sin(θ) = √2/2, cos(θ) = -√2/2

sin(θ) = -√2/2, cos(θ) = √2/2

sin(θ) = √2/2, cos(θ) = √2/2

sin(θ) = -√2/2, cos(θ) = -√2/2

#15

What is the sine of an angle θ in the fourth quadrant if cos(θ) = 5/13?

12/13

-12/13

5/13

-5/13

#16

If sin(θ) = 3/5 in the second quadrant, what is cos(θ)?

4/5

-4/5

√34/5

-√34/5

#17

For the angle θ in standard position, if the terminal side of θ passes through the point (-4, -3), what is the value of sin(θ)?

3/5

-3/5