Solving an equation using the half angle formula of sine

The video tutorial covers solving a trigonometric equation involving sine and cosine functions. The instructor begins by introducing the problem and discussing the need to rewrite the equation using trigonometric identities. The process involves isolating terms and using algebraic methods to simplify the equation. The instructor explains the importance of isolating the square root before squaring both sides. Finally, the equation is factored, and solutions are found within a specified interval. The tutorial emphasizes the use of algebraic techniques and trigonometric identities to solve complex equations.

What is the first step in solving the equation involving sine and cosine functions?

• Add a constant to both sides

• Rewrite using known trigonometric formulas

• Directly factor the equation

• Square both sides immediately

Why is it important not to square both sides of an equation prematurely?

• It is mathematically incorrect

• It makes the equation unsolvable

• It can introduce extraneous solutions

• It simplifies the equation too much

What operation is performed to eliminate the square root in the equation?

• Adding a constant to both sides

• Dividing both sides by a constant

• Squaring both sides

• Multiplying both sides by a constant

After eliminating the square root, what type of equation is formed?

• Cubic equation

• Exponential equation

• Linear equation

• Quadratic equation

What is the next step after forming a quadratic equation in the problem?

• Graph the equation

• Use substitution to simplify

• Factor the equation into binomials

• Solve using the quadratic formula

What are the solutions for cosine of X in the interval 0 to 2π?

• π/4 and 3π/4

• π/3 and 2π/3

• π/6 and 5π/6

• π/2 and 3π/2

At what value of X does cosine equal 1 in the interval 0 to 2π?

• 2π

• 0

• π

• π/2