Trigonometric Identities and Equations

This video tutorial covers fundamental trigonometric identities, including sine, cosine, and tangent relationships. It explains the Pythagorean identity and demonstrates how to apply these identities to solve trigonometric equations. The tutorial also explores solving quadratic trigonometric equations using the quadratic formula, providing examples and step-by-step solutions.

Which trigonometric identity expresses tan(theta) in terms of sine and cosine?

• tan(theta) = 1/sine(theta)

• tan(theta) = sine(theta)/cos(theta)

• tan(theta) = cos(theta)/sine(theta)

• tan(theta) = 1/cos(theta)

What is the Pythagorean identity involving sine and cosine?

• sine(theta) - cos(theta) = 1

• sine(theta) + cos(theta) = 1

• sine^2(theta) - cos^2(theta) = 1

• sine^2(theta) + cos^2(theta) = 1

In the example of solving 3 sine(theta) = 4 cos(theta), what is the first step?

• Add sine(theta) to both sides

• Divide both sides by sine(theta)

• Divide both sides by cos(theta)

• Multiply both sides by cos(theta)

What is the angle obtained when solving tan(theta) = 4/3 using the CAST diagram?

• 53.1 degrees

• 90 degrees

• 270 degrees

• 180 degrees

When solving 4 sine^2(theta) = 2 cos(theta), what substitution is used for sine^2(theta)?

• 1 + cos^2(theta)

• 1 - cos^2(theta)

• cos^2(theta) - 1

• cos^2(theta) + 1

What type of equation is formed after substituting in the example 4 sine^2(theta) = 2 cos(theta)?

• Exponential equation

• Quadratic equation

• Linear equation

• Logarithmic equation

What are the two angles obtained from solving the quadratic equation in the final example?

• 45 degrees and 135 degrees

• 90 degrees and 270 degrees

• 38.7 degrees and 321.3 degrees

• 60 degrees and 300 degrees