Trigonometric Identities and Formulas

The video tutorial covers trigonometric identities, focusing on sum, difference, and double angle formulas. It provides examples of solving problems using these identities and includes a proof of the formulas. The tutorial also demonstrates solving trigonometric equations and concludes with a shoutout to students.

What is the formula for the sine of the sum of two angles?

• sin(α + β) = cos(α)sin(β) - sin(α)cos(β)

• sin(α + β) = sin(α)cos(β) + cos(α)sin(β)

• sin(α + β) = cos(α)cos(β) - sin(α)sin(β)

• sin(α + β) = sin(α)sin(β) - cos(α)cos(β)

What is the formula for the cosine of the difference of two angles?

• cos(α - β) = sin(α)sin(β) - cos(α)cos(β)

• cos(α - β) = sin(α)cos(β) + cos(α)sin(β)

• cos(α - β) = cos(α)cos(β) - sin(α)sin(β)

• cos(α - β) = cos(α)cos(β) + sin(α)sin(β)

How can you find the exact value of sin(75°) using sum identities?

• sin(75°) = sin(30° + 45°)

• sin(75°) = sin(45° + 30°)

• sin(75°) = sin(60° + 15°)

• sin(75°) = sin(90° - 15°)

What is the exact value of cos(15°) using difference identities?

• cos(15°) = cos(45° - 30°)

• cos(15°) = cos(60° - 45°)

• cos(15°) = cos(30° - 15°)

• cos(15°) = cos(90° - 75°)

What is the purpose of using the distance formula in the proof of sum and difference identities?

• To find the distance between two points on the unit circle

• To calculate the area of a triangle

• To prove the Pythagorean theorem

• To show the relationship between angles and their trigonometric functions

What is the double angle formula for sine?

• sin(2α) = sin(α)cos(α) + cos(α)sin(α)

• sin(2α) = 2sin(α)cos(α)

• sin(2α) = sin²(α) - cos²(α)

• sin(2α) = 2cos(α)sin(α)

Which of the following is a correct double angle formula for cosine?

• All of the above

• cos(2α) = 1 - 2sin²(α)

• cos(2α) = 2cos²(α) - 1

• cos(2α) = cos²(α) - sin²(α)

How do you solve the equation 2sin(x)cos(x) = cos(x)?

• By factoring out cos(x)

• By subtracting sin(x) from both sides

• By dividing both sides by cos(x)

• By adding sin(x) to both sides

What is the solution to the equation cos(2x) = 2cos²(x) - 1?

• x = π/6, 5π/6, 7π/6, 11π/6

• x = π/4, 3π/4, 5π/4, 7π/4

• x = π/3, 2π/3, 4π/3, 5π/3

• x = π/2, 3π/2

What is the simplified form of cos(2x) using the identity cos(2x) = 1 - 2sin²(x)?

• cos(2x) = 2sin²(x) - 1

• cos(2x) = cos²(x) - sin²(x)

• cos(2x) = 2cos²(x) - 1

• cos(2x) = 1 - 2sin²(x)