Trigonometric Functions and Identities

This video tutorial covers solving trigonometric equations using various strategies. It begins with an introduction to the topic and explores methods such as using conjugates and substitutions. The video also delves into solving quadratic trigonometric equations and applying double angle identities. Throughout, the instructor provides step-by-step explanations and sketches to aid understanding, ensuring that viewers can follow along and apply these techniques to similar problems.

What is the first step suggested to solve the initial trigonometric equation?

• Multiply by the conjugate of the denominator

• Use a calculator

• Convert to radians

• Add the fractions directly

What is the value of cosine theta when it equals 1/2?

• 45 degrees

• 60 degrees

• 90 degrees

• 30 degrees

In which quadrants is cosine positive?

• First and second

• Second and third

• Third and fourth

• First and fourth

What substitution is made for secant squared x in the second equation?

• Sine squared x + 1

• Cotangent squared x + 1

• Cosine squared x + 1

• Tangent squared x + 1

Which reference angle is used when tangent x equals -1?

• 30 degrees

• 60 degrees

• 45 degrees

• 90 degrees

What is the approximate radian measure for the inverse tangent of 3?

• 1.25 radians

• 2.5 radians

• 3.14 radians

• 0.75 radians

Which identity is used for sine 2x in the double angle problem?

• Sine squared x - cosine squared x

• 1 - 2 sine squared x

• 2 cosine squared x - 1

• 2 sine x cosine x

What is the common factor used to simplify the double angle equation?

• Cosine x

• Secant x

• Sine x

• Tangent x

What is the reference angle for tangent x equals 1?

• 90 degrees

• 45 degrees

• 60 degrees

• 30 degrees

In which quadrants is tangent positive?

• First and second

• Third and fourth

• Second and third

• First and third