Trigonometric Identities and Formulas

The video tutorial covers the sum and product formulas in trigonometry, demonstrating how to convert between sum to product and product to sum using trigonometric identities. It includes examples, proofs, and verification of identities, providing a comprehensive understanding of these concepts.

What is the first step in converting the formula for cosine(a) sine(b)?

• Replace beta with alpha and alpha with beta

• Simplify the equation

• Factor out a negative one

• Use the double angle identity

In the example of converting sum to product, what is the result of 2x over 2?

• 4x

• x

• 1

• 2x

What is the result of applying the sum-to-product formula to cosine(a) + cosine(b)?

• cosine(a) cosine(b) - sine(a) sine(b)

• sine(a) sine(b) + cosine(a) cosine(b)

• 2 sine((a+b)/2) sine((a-b)/2)

• 2 cosine((a+b)/2) cosine((a-b)/2)

When converting sine(a) sine(b) to a sum, what is the first step?

• Set a equal to the first argument

• All of the above

• Set b equal to the second argument

• Multiply by one half

What is the simplified form of 2 sine(2x) cosine(x)?

• sine(3x)

• 2 sine(x) cosine(2x)

• cosine(3x)

• 4 sine(x) cosine(x)

What is the result of applying the product-to-sum formula to sine(a) cosine(b)?

• 1/2 [sine(a+b) + sine(a-b)]

• 1/2 [sine(a+b) - sine(a-b)]

• 1/2 [cosine(a+b) - cosine(a-b)]

• 1/2 [cosine(a+b) + cosine(a-b)]

How do you verify a trigonometric identity using sum-to-product formulas?

• Use the unit circle

• Apply the Pythagorean identity

• Simplify both sides separately

• Graph the original and simplified functions

Which function is used to verify the identity of tangent(x - y)?

• sine(x) / cosine(y)

• tangent(x) - tangent(y)

• tangent(x) - tangent(y) / 1 + tangent(x) tangent(y)

• cosine(x) / sine(y)

How do you simplify the expression 2 sine(2x) cosine(x)?

• Apply the Pythagorean identity

• Use the double angle identity

• Use the unit circle

• Factor out a common term

What is the final step in proving a trigonometric identity?

• Graph the functions

• Simplify both sides

• Verify the identity using known values

• All of the above