Trigonometric Identities and Formulas

This video tutorial covers trigonometry topics, focusing on solving equations using double angle formulas and proving trigonometric identities. Part A involves solving the equation 7 cos(θ/2) = 10 sin(θ) by converting angles and using the sine double angle formula. Part B focuses on proving a trigonometric identity involving secant and tangent functions. The video concludes with a summary and a call to action to subscribe for more practical math content.

What is the main topic discussed in the video?

• Geometry and Statistics

• Trigonometry and Double Angle Formulas

• Algebra and Calculus

• Probability and Combinatorics

In Part A, what equation are we solving?

• 2 tan(θ) = 4 sec(θ/2)

• 7 cos(θ/2) = 10 sin(θ)

• 5 sin(θ) = 3 cos(θ/2)

• 9 sin(θ/2) = 6 cos(θ)

What formula is used to convert angles in Part A?

• Secant Double Angle Formula

• Tangent Double Angle Formula

• Cosine Double Angle Formula

• Sine Double Angle Formula

What is the range of θ/2 after conversion?

• π to 2π

• 0 to 2π

• 0 to π

• 0 to π/2

When is cosine equal to zero?

• At 0 and π

• At π/2 and 3π/2

• At π/3 and 2π/3

• At π/4 and 3π/4

What is the basic angle α when sin(θ/2) = 7/20?

• sec⁻¹(7/20)

• sin⁻¹(7/20)

• cos⁻¹(7/20)

• tan⁻¹(7/20)

In which quadrants is sine positive?

• First and Third

• Second and Fourth

• First and Second

• Third and Fourth

What is the final solution for θ in Part A?

• 0.715, π, 5.57

• 0.25, π/4, 3π/4

• 1.57, 3.14, 6.28

• 0.5, π/2, 3π/2

What is the goal of Part B?

• Calculate the derivative of a function

• Find the range of a function

• Prove a trigonometric identity

• Solve a trigonometric equation

Which trigonometric functions are involved in the identity proof?

• Sine and Tangent

• Tangent and Secant

• Sine and Cosine

• Cosecant and Cotangent