Exploring the Unit Circle Fundamentals

What is the radius of the unit circle?

• 2

• 1

• 0.5

• 10

Which mnemonic helps remember trigonometric ratios?

• PEMDAS

• ROYGBIV

• None

• SOHCAHTOA

What does the sine of an angle represent in a right triangle within the unit circle?

• Adjacent over hypotenuse

• Opposite over adjacent

• Hypotenuse over opposite

• Opposite over hypotenuse

What is the cosine of an angle equal to in the context of the unit circle?

• Opposite side length

• Hypotenuse length

• Adjacent side length

• None of the above

What is the hypotenuse length of the triangle drawn within the unit circle?

• 1

• 2

• 1.5

• 0.5

How is the tangent of an angle calculated in a right triangle?

• Sine over cosine

• Cosine over sine

• Opposite over adjacent

• Adjacent over opposite

What coordinates represent any point on the unit circle?

• (tan(θ), cot(θ))

• (sin(θ), cos(θ))

• (cos(θ), sin(θ))

• (sec(θ), csc(θ))

What trigonometric function is described as opposite over adjacent in a right triangle?

• Tangent

• Cosine

• Sine

• Cotangent

What does the Pythagorean identity in the unit circle state?

• sec²(θ) - tan²(θ) = 1

• sin²(θ) + cos²(θ) = 1

• tan²(θ) + cot²(θ) = 1

• csc²(θ) - cot²(θ) = 1

Which theorem is used to derive the Pythagorean identity in the unit circle?

• Euclid's theorem

• Pythagorean theorem

• Fermat's Last Theorem

• Theorem of Thales