Exploring Trigonometric Identities and Their Applications

What is the primary reason for establishing trigonometric identities?

• To make trigonometry more complex

• To simplify and speed up the manipulation of recurring trigonometric expressions

• To create more formulas to memorize

• To confuse students

In the mnemonic SOH-CAH-TOA, what does 'CAH' stand for?

• Cosine is adjacent over hypotenuse

• Cosine is opposite over hypotenuse

• Cosine is hypotenuse over adjacent

• Cosine is hypotenuse over opposite

What is the reciprocal of the sine function?

• Secant

• Cosecant

• Cotangent

• Tangent

Which identity states that tangent of theta is equal to sine of theta divided by cosine of theta?

• Reciprocal identity

• Quotient identity

• Pythagorean identity

• Even-odd identity

What is the first Pythagorean identity?

• tan^2(theta) + 1 = sec^2(theta)

• 1 + cot^2(theta) = csc^2(theta)

• cos^2(theta) + sin^2(theta) = 1

• sin^2(theta) - cos^2(theta) = 1

Which trigonometric functions are considered even?

• Sine and cosecant

• Cosine and secant

• Sine and tangent

• Tangent and cotangent

What is the co-function identity for sine?

• sin(pi/2 - theta) = csc(theta)

• sin(pi/2 - theta) = cos(theta)

• sin(pi/2 - theta) = sin(theta)

• sin(pi/2 - theta) = tan(theta)

What is the sum-difference identity for sine of alpha plus beta?

• sin(alpha + beta) = cos(alpha)cos(beta) + sin(alpha)sin(beta)

• sin(alpha + beta) = sin(alpha)cos(beta) - cos(alpha)sin(beta)

• sin(alpha + beta) = sin(alpha)cos(beta) + cos(alpha)sin(beta)

• sin(alpha + beta) = cos(alpha)cos(beta) - sin(alpha)sin(beta)

Which double-angle identity for sine is most commonly used?

• sin(2theta) = 2sin^2(theta) - 1

• sin(2theta) = 1 - 2cos^2(theta)

• sin(2theta) = sin^2(theta) - cos^2(theta)

• sin(2theta) = 2sin(theta)cos(theta)

What is the product-to-sum identity for sine(alpha) * sine(beta)?

• 1/2 [sin(alpha - beta) - sin(alpha + beta)]

• 1/2 [sin(alpha + beta) + sin(alpha - beta)]

• 1/2 [cos(alpha + beta) + cos(alpha - beta)]

• 1/2 [cos(alpha - beta) - cos(alpha + beta)]