Exploring Trig Identities and Reciprocals

What is the cosine of an angle in the unit circle?

• The x-coordinate of the point

• The ratio of the opposite side to the hypotenuse

• The y-coordinate of the point

• The ratio of the adjacent side to the opposite side

What does the tangent of an angle represent in the unit circle?

• The ratio of the y-coordinate to the x-coordinate

• The ratio of the x-coordinate to the y-coordinate

• The ratio of the hypotenuse to the adjacent side

• The ratio of the adjacent side to the hypotenuse

What is the reciprocal of the sine function?

• Cosecant

• Secant

• Cotangent

• Cosine

Which identity represents the cotangent function as a reciprocal?

• Cosecant over secant

• Sine over cosine

• Secant over cosecant

• Cosine over sine

What does the Pythagorean identity state for a unit circle?

• sec^2(theta) - tan^2(theta) = 1

• tan^2(theta) + cot^2(theta) = 1

• csc^2(theta) - cot^2(theta) = 1

• sin^2(theta) + cos^2(theta) = 1

What is the result of dividing the Pythagorean identity by cos^2(theta)?

• sec^2(theta) - 1 = tan^2(theta)

• 1 + cot^2(theta) = csc^2(theta)

• sin^2(theta) + 1 = csc^2(theta)

• tan^2(theta) + 1 = sec^2(theta)

How can the expression 'sin(x) * sec(x)' be simplified?

• sin(x)

• tan(x)

• cot(x)

• cos(x)

What does the expression 'cos(x) / sin(x)' simplify to?

• Csc(x)

• Cot(x)

• Tan(x)

• Sec(x)

What is the simplified form of 'tan(x) * csc(x) * cos(x)'?

• cot(x)

• 1

• sec(x)

• sin(x)

If 'sin^2(x) + cot^2(x)' is transformed using trig identities, what does it simplify to?

• 1

• csc^2(x)

• sec^2(x)

• cos^2(x)