Complementary Angles and Trigonometric Expressions

The video tutorial explains how to simplify trigonometric expressions using the relationship between sine and cosine of complementary angles. It outlines three key steps: identifying complementary angles, substituting cofunctions, and simplifying the expression. Two examples are provided: one simplifies an expression, and the other solves for x using complementary angles. The tutorial emphasizes the equality of sine and cosine for complementary angles and demonstrates the process with practical examples.

What is the main focus of this lesson on trigonometric expressions?

• Learning about tangent and cotangent functions

• Simplifying expressions using complementary angles

• Exploring the unit circle

• Understanding the Pythagorean theorem

If alpha and beta are complementary angles, which of the following is true?

• Cosine of alpha equals cosine of beta

• Sine of alpha equals cosine of beta

• Sine of alpha equals sine of beta

• Sine of alpha equals tangent of beta

What is the first step in simplifying trigonometric expressions?

• Use the Pythagorean identity

• Convert to radians

• Look for complementary angles

• Apply the angle sum identity

In the example problem, what is the simplified form of sine of alpha plus cosine of beta divided by cosine of beta?

• 1

• 2

• Tangent of alpha

• Sine of beta

What is the final simplified form of sine of alpha plus cosine of beta divided by cosine of alpha?

• Sine of alpha

• 2 times the tangent of alpha

• Tangent of beta

• Cosine of alpha

In solving for x, what equation is set up to find the complementary angles?

• x + 13 = 2x - 19

• x + 13 + 2x - 19 = 90

• x + 13 = 90

• 2x - 19 = 90

What is the value of x when solving the equation sine of (x + 13) equals cosine of (2x - 19)?

• 45

• 32

• 60

• 90

After solving for x, what is the sine of 45 degrees equal to?

• Cosine of 30 degrees

• Cosine of 90 degrees

• Cosine of 45 degrees

• Sine of 60 degrees

What is the approximate value of sine and cosine of 45 degrees?

• 0.866

• 0.5

• 0.707

• 1

What concept is used to verify the solution for x in the trigonometric equation?

• Pythagorean identity

• Complementary angles

• Unit circle

• Angle sum identity