Trigonometric Functions and Identities

The video tutorial covers trigonometric identities, focusing on sum and difference identities, co-function identities, and even and odd properties of sinusoidal functions. It explains how to find exact trigonometric values using these identities and demonstrates graphing techniques to verify identities. The tutorial also includes proving various trigonometric identities and concludes with a summary and encouragement to subscribe.

What is the basis for the co-function identities?

• Adjacent angles

• Vertical angles

• Complementary angles

• Supplementary angles

Why is sine of an angle equal to cosine of its complement?

• Because they are supplementary

• Because they are vertical angles

• Because they are adjacent angles

• Because they are complementary

What is the property of sine when it is considered an odd function?

• sine(-x) = sine(x)

• sine(-x) = -cosine(x)

• sine(-x) = -sine(x)

• sine(-x) = cosine(x)

What is the property of cosine when it is considered an even function?

• cosine(-x) = -sine(x)

• cosine(-x) = cosine(x)

• cosine(-x) = sine(x)

• cosine(-x) = -cosine(x)

How can you find the exact value of cosine(π/12)?

• Using the sum formula for cosine

• Using the difference formula for cosine

• Using the sum formula for sine

• Using the difference formula for sine

What is the sum formula for sine?

• sine(x + y) = sine(x)cosine(y) - cosine(x)sine(y)

• sine(x + y) = sine(x)cosine(y) + cosine(x)sine(y)

• sine(x + y) = cosine(x)cosine(y) + sine(x)sine(y)

• sine(x + y) = cosine(x)cosine(y) - sine(x)sine(y)

What is the co-function identity for secant?

• sec(π/2 - θ) = tangent(θ)

• sec(π/2 - θ) = cotangent(θ)

• sec(π/2 - θ) = sec(θ)

• sec(π/2 - θ) = cosecant(θ)

What is the co-function identity for tangent?

• tangent(π/2 - θ) = cosecant(θ)

• tangent(π/2 - θ) = secant(θ)

• tangent(π/2 - θ) = tangent(θ)

• tangent(π/2 - θ) = cotangent(θ)

How can you verify trigonometric identities using graphing calculators?

• By solving the equations algebraically

• By using the unit circle

• By comparing the graphs of the original and simplified functions

• By using the Pythagorean theorem

What is the equivalent expression for sine(π/4 + x)?

• sine(π/4 - x)

• cosine(π/4 - x)

• cosine(π/4 + x)

• sine(π/4 + x)