Trigonometric Functions and Identities

This video tutorial covers trigonometric identities, starting with basic concepts and moving to more advanced problem-solving techniques. It explains the relationships between sine, cosine, and tangent, and demonstrates how to use these identities to solve equations. The video also provides examples and encourages viewers to try exam questions for practice.

What is the exact value of sine 60 degrees?

• √3/2

• 1

• 1/2

• √2/2

What is the exact value of cosine 60 degrees?

• 1

• √2/2

• √3/2

• 1/2

What is the result of dividing sine 60 by cosine 60?

• 1

• √3

• 1/√3

• 2

Which identity is demonstrated by dividing sine by cosine?

• Reciprocal Identity

• Pythagorean Identity

• Quotient Identity

• Even-Odd Identity

What is the Pythagorean identity?

• cos²θ - sin²θ = 1

• 1 + tan²θ = sec²θ

• sinθ/cosθ = tanθ

• sin²θ + cos²θ = 1

How can the Pythagorean identity be rearranged to express sin²θ?

• 1 - cos²θ

• cos²θ - 1

• 1 + cos²θ

• cos²θ

How can the Pythagorean identity be rearranged to express cos²θ?

• 1 - sin²θ

• sin²θ

• sin²θ - 1

• 1 + sin²θ

In the example problem, what is the first step to simplify 2sin²θ + cos²θ?

• Multiply by 2

• Replace sin²θ with 1 - cos²θ

• Subtract sin²θ

• Add cos²θ

What is the result of simplifying 2sin²θ + cos²θ using the identity?

• cos²θ - 1

• 1 + sin²θ

• 2 - cos²θ

• sin²θ + 1

In the second example problem, what is the common denominator used?

• 1

• sinθcosθ

• cosθ

• sinθ