Trigonometric Identities and Functions

This video tutorial covers solving trigonometric equations using various strategies, including multiplying by conjugates, using common denominators, and applying double angle identities. It explains how to solve equations involving cosine and tangent functions, and how to find solutions using reference angles and the unit circle. The tutorial also demonstrates solving quadratic trig equations and using calculators for non-standard angles.

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

• Multiply by the conjugate of the denominator

• Convert to radians

• Add the fractions directly

• Use a calculator

What identity is used to simplify 1 - sin²(theta)?

• sin²(theta)

• tan²(theta)

• cos²(theta)

• sec²(theta)

In which quadrants is cosine positive?

• Second and third

• First and second

• First and fourth

• Third and fourth

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

• tan²(X) + 1

• sin²(X) + 1

• cot²(X) + 1

• cos²(X) + 1

Which reference angle is associated with a tangent value of -1?

• 60 degrees

• 90 degrees

• 30 degrees

• 45 degrees

What tool is suggested for solving tan(X) = 3?

• Ruler

• Scientific calculator

• Protractor

• Graphing calculator

What identity is used to replace sin(2X) in the double angle equation?

• 1 - 2 sin²(X)

• 2 sin(X) cos(X)

• 2 cos²(X) - 1

• sin²(X) - cos²(X)

Which identity is chosen for cos(2X) to simplify the equation?

• 2 cos²(X) - 1

• 2 sin(X) cos(X)

• cos²(X) - sin²(X)

• 1 - 2 sin²(X)

What is the result when dividing sin(X) by cos(X)?

• tan(X)

• csc(X)

• sec(X)

• cot(X)

Which angles on the unit circle have a cosine value of zero?

• 0 and π

• π/2 and 3π/2

• π/4 and 5π/4

• π/3 and 4π/3