Trigonometric Functions and Equations

This video tutorial covers solving trigonometric equations, focusing on sine, cosine, and tangent functions. It explains the importance of memorizing trigonometric facts and reference angles. The video provides detailed steps for evaluating arc sine, solving cosine and tangent equations, and understanding the differences in their periods. Several examples and practice problems are included to reinforce the concepts and demonstrate how to find solutions within specified intervals.

What is the first step in solving trigonometric equations?

• Understand the range of inverse functions

• Memorize the unit circle

• Learn the Pythagorean identities

• Memorize key trigonometric facts

How do you evaluate the arcsine of a number?

• Find the angle whose cosine is the given number

• Find the angle whose tangent is the given number

• Find the angle whose secant is the given number

• Find the angle whose sine is the given number

What is the range restriction for the arcsine function?

• 0 to π

• -π/2 to π/2

• 0 to 2π

• -π to π

How many solutions can a sine equation have on the interval from 0 to 2π?

• One

• Two

• Three

• Infinitely many

What is the period of the tangent function?

• π

• 2π

• π/2

• 4π

When solving a tangent equation, how many equations are needed to represent all solutions?

• Four

• One

• Three

• Two

What is the reference angle for cosine when it equals √2/2?

• π/4

• π/6

• π/3

• π/2

How do you indicate that the entire sine function is squared?

• sin^2(x)

• (sin(x))^2

• 2sin(x)

• sin(x)^2

What should you avoid doing when solving equations involving trigonometric functions?

• Subtracting terms

• Adding terms

• Dividing by a trigonometric function

• Multiplying terms