Untitled Quiz

Podcast

Play an AI-generated podcast conversation about this lesson

Download our mobile app to listen on the go

Get App

Questions and Answers

What is the correct definition of the sine function based on the right triangle definition?

sin(θ) = adjacent / hypotenuse
sin(θ) = opposite / adjacent
sin(θ) = opposite / hypotenuse (correct)
sin(θ) = hypotenuse / opposite

Which of the following statements correctly represents the domain of the tangent function?

θ can be any angle except 90 degrees
θ cannot equal nπ, where n is any integer
θ can be any angle
θ cannot equal n + π, where n is any integer (correct)

What is the period of the function cos(ωθ)?

2πω
2π
ω (correct)
π

What does the cosecant function equal in terms of sine?

csc(θ) = hypotenuse / opposite (D) Signup and view all the answers

Which of the following functions has the same periodicity as the sine function?

csc(θ) (D) Signup and view all the answers

What is the relationship between secant and cosine?

sec(θ) = 1 / cos(θ) (D) Signup and view all the answers

In terms of the unit circle, which coordinates correspond to the sine function?

(cos(θ), sin(θ)) (B) Signup and view all the answers

Which of the following is NOT defined for the cosecant function?

nπ where n is any integer (B) Signup and view all the answers

Which of the following statements about the range of the sine function is true?

The sine function ranges from -1 to 1. (C) Signup and view all the answers

Which identity correctly represents the relationship between tangent and cotangent?

tan(θ) = 1/cot(θ) (B) Signup and view all the answers

Which of the following ranges is correct for the cosecant function?

csc(θ) ≥ 1 and csc(θ) ≤ −1 (D) Signup and view all the answers

What is the correct expression to define tan(θ) using sine and cosine?

tan(θ) = sin(θ)/cos(θ) (B) Signup and view all the answers

The inverse function sin^(-1)(x) is defined for which domain?

−1 ≤ x ≤ 1 (D) Signup and view all the answers

What is the formula for the sine of a double angle?

sin(2θ) = 2sin(θ)cos(θ) (D) Signup and view all the answers

Which of the following statements about the periodic properties of sine is correct?

sin(θ + 2π) = sin(θ) (D) Signup and view all the answers

In which scenario is the cosecant function undefined?

When sin(θ) = 0 (B) Signup and view all the answers

What is the result of applying the Even/Odd formula to the cosine function?

cos(-θ) = cos(θ) (B) Signup and view all the answers

What is the domain of the function tan^(-1)(x)?

−∞ < x < ∞ (A) Signup and view all the answers

Which identity accurately describes the relationship between the cosine and sine of complementary angles?

Both B and C are correct. (B) Signup and view all the answers

Which of the following is not a Pythagorean identity?

tan²(θ) + 1 = cot²(θ) (B) Signup and view all the answers

Which of the following is the definition of the cosecant function?

csc(θ) = 1/sin(θ) (D) Signup and view all the answers

The formula for the secant function is derived from which basic function?

cos(θ) (A) Signup and view all the answers

Flashcards

Sine of an angle

In a right triangle, the ratio of the side opposite to the angle to the hypotenuse.

Cosine of an angle

In a right triangle, the ratio of the side adjacent to the angle to the hypotenuse.