Exploring Trig Identities for AP Calculus

What is the primary reason trigonometric identities are memorized in calculus?

• To solve them faster during exams

• To understand their historical context

• To create new identities during tests

• To avoid learning them at all

What does the Pythagorean identity state?

• sin(theta) * cos(theta) = 1

• sin^2(theta) + cos^2(theta) = 1

• tan(theta) + cot(theta) = 1

• sec(theta) * csc(theta) = 1

What is the result of applying the Pythagorean identity to the unit circle?

• sin(theta) * cos(theta) = 1

• sin^2(theta) + cos^2(theta) = 1

• tan(theta) + cot(theta) = 1

• sec(theta) * csc(theta) = 1

How is the cosine difference identity derived?

• Through integration of sine functions

• Using the distance formula on the unit circle

• By subtracting one cosine function from another

• By differentiating the tangent function

What is the formula for cosine of u minus v?

• cos(u-v) = sin(u) * cos(v) + cos(u) * sin(v)

• cos(u-v) = sin(u) * sin(v) - cos(u) * cos(v)

• cos(u-v) = cos(u) * cos(v) + sin(u) * sin(v)

• cos(u-v) = cos(u) * cos(v) - sin(u) * sin(v)

What property of trigonometric functions is used to derive the cosine sum identity?

• Periodicity

• Even and odd nature

• Amplitude adjustments

• Phase shifts

Which identity represents cosine of u plus v?

• cos(u+v) = sin(u) * sin(v) - cos(u) * cos(v)

• cos(u+v) = cos(u) * cos(v) + sin(u) * sin(v)

• cos(u+v) = cos(u) * cos(v) - sin(u) * sin(v)

• cos(u+v) = sin(u) * cos(v) + cos(u) * sin(v)

What does the cofunction identity for sine and cosine state?

• sin(theta) = cos(pi/2 - theta)

• cos(theta) = sin(pi/2 + theta)

• cos(theta) = cos(pi/2 - theta)

• sin(theta) = sin(pi/2 - theta)

How can sine of u plus v be expressed using cofunction identities?

• sin(u+v) = sin(u) * cos(v) + cos(u) * sin(v)

• sin(u+v) = sin(u) * sin(v) - cos(u) * cos(v)

• sin(u+v) = cos(u) * cos(v) + sin(u) * sin(v)

• sin(u+v) = cos(u) * cos(v) - sin(u) * sin(v)

Which identity is used to simplify expressions involving sine and cosine of summed angles?

• Even and odd identities

• Cofunction identities

• Sum and difference identities

• Pythagorean identity