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Trigonometry and Unit Circle Concepts Quiz

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What is the value of sin(90°)?

Explanation

Sine of 90° is the maximum value in the unit circle.

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

Explanation

Cosine is the x-coordinate in the unit circle.

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

-1

Explanation

Sine of 270° is the lowest value in the unit circle.

What is the exact value of cos(45°)?

√2/2

Explanation

Cosine of 45° is a commonly known value.

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

2π

Explanation

The sine function repeats every 2π radians.

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

-1 ≤ sin(θ) ≤ 1

Explanation

Sine values range between -1 and 1 inclusive.

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

tan(θ) = sin(θ)/cos(θ)

Explanation

Tangent is defined as sine over cosine.

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

-1/2

Explanation

Cosine of 120° is a negative value in the unit circle.

Which of the following represents the Pythagorean identity?

All of the above

Explanation

All the given identities are part of the Pythagorean identity.

#10

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

III

Explanation

Negative cosine places θ in the third quadrant.

#11

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

45°

Explanation

Tangent is 1 at 45°.

#12

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

390°

Explanation

Adding 360° keeps the terminal side the same.

#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?

Explanation

Arc length corresponds directly to the angle in radians.

#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

Explanation

Corresponding values in the third quadrant.

#15

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

-12/13

Explanation

Sine is negative in the fourth quadrant.

#16

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

-4/5

Explanation

Cosine is negative in the second quadrant.

#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

Explanation

Sine is the y-coordinate on the unit circle.

Trigonometry and Unit Circle Concepts Quiz

What is the value of sin(90°)?

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

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

What is the exact value of cos(45°)?

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

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

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

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

Which of the following represents the Pythagorean identity?

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

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

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

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?

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

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

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

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)?

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