Pre-Calculus - Using Double Angle Formulas to Help Solve for Solutions to an Equation

The video tutorial covers solving trigonometric equations involving cosine. It begins with an introduction to the problem and reviews methods such as reverse operations and factoring. The instructor then applies multiple angle formulas to simplify the equation, using identities to express everything in terms of cosine. Finally, the equation is factored, and solutions are found using the unit circle, focusing on solutions within one revolution.

What is the first step in solving the equation cosine of 2X minus cosine of X equals 0?

• Use reverse order of operations

• Combine like terms

• Graph the equation

• Apply the quadratic formula

Which formula is chosen to express cosine of 2X in terms of cosine and sine?

• Cosine squared plus sine squared

• Sine squared minus cosine squared

• Cosine plus sine

• Cosine squared minus sine squared

What identity is used to replace sine squared of X in the equation?

• Sine equals cosine

• Cosine squared equals 1 minus sine squared

• Tangent equals sine over cosine

• Sine squared equals 1 minus cosine squared

After substitution, what type of problem does the equation become?

• A graphing problem

• A linear equation

• A factoring problem

• A differential equation

What is the value of cosine of X when X equals 0 on the unit circle?

• 0

• 1

• 1/2

• -1

At which angles is cosine of X equal to -1/2 on the unit circle?

• 0 and π

• π/3 and 2π/3

• 2π/3 and 4π/3

• π/2 and 3π/2

Why are only solutions between 0 and 2π considered?

• To find all possible solutions

• To focus on one revolution of the unit circle

• To avoid complex numbers

• To simplify the problem