Formulas for Trigonometric Functions: Sum/Difference, Double/Half-Angle, Prod-to-Sum/Sum-to-Prod

The video tutorial covers essential trigonometric formulas, including sum and difference, double angle, power-reducing, half-angle, and product-to-sum formulas. It explains their derivations, applications, and how to use them to find exact values of trigonometric functions. The tutorial emphasizes the importance of these formulas in solving trigonometric problems and verifying identities.

What is the purpose of the sum and difference formulas for sine and cosine?

• To calculate the tangent of an angle

• To find the sine or cosine of an angle that is the sum or difference of two other angles

• To determine the exact value of an angle on the unit circle

• To convert angles from degrees to radians

How can the double angle formula for cosine be expressed?

• cos(2θ) = cos²θ - sin²θ

• cos(2θ) = 2sinθcosθ

• cos(2θ) = 1 - tan²θ

• cos(2θ) = sin²θ + cos²θ

What is the double angle formula for sine?

• sin(2θ) = 2sinθcosθ

• sin(2θ) = sin²θ - cos²θ

• sin(2θ) = 1 - 2sin²θ

• sin(2θ) = 2tanθ/(1-tan²θ)

What is a power-reducing formula used for?

• To express sine squared theta in terms of cosine theta

• To find the tangent of an angle

• To simplify complex numbers

• To convert radians to degrees

What is the half-angle formula for sine?

• sin(x/2) = ±√((1-tan(x))/2)

• sin(x/2) = ±√((1+cos(x))/2)

• sin(x/2) = ±√((1-cos(x))/2)

• sin(x/2) = ±√((1+tan(x))/2)

What do product-to-sum formulas do?

• Convert the product of two trig functions into a sum or difference

• Convert the sum of two angles into a product

• Calculate the sine of a sum

• Determine the cosine of a difference

How can the expression sin(9x) + sin(5x) be rewritten using sum-to-product formulas?

• cos(9x) - cos(5x)

• 2sin(7x)cos(2x)

• 2cos(7x)sin(2x)

• sin(14x) + sin(4x)