Trigonometric Identities and Functions

This video tutorial covers trigonometric identities, starting with an introduction to their relationship with the unit circle. It explains the Pythagorean identity and demonstrates how to manipulate and derive other identities. The tutorial also introduces reciprocal trig identities and provides methods for simplifying trig expressions. Finally, it shows how to solve trigonometric equations using these identities and simplification techniques.

What is the Pythagorean identity in trigonometry?

• 1 + cot²θ = csc²θ

• cos²θ + sin²θ = 1

• sin²θ - cos²θ = 1

• tan²θ + 1 = sec²θ

How can you express cos²θ using the Pythagorean identity?

• 1 + cos²θ

• 1 - sin²θ

• 1 + sin²θ

• sin²θ - 1

Which identity is derived by dividing the Pythagorean identity by sin²θ?

• 1 + cot²θ = csc²θ

• tan²θ + 1 = sec²θ

• 1 - sin²θ = cos²θ

• cos²θ + sin²θ = 1

What is the result of dividing the Pythagorean identity by cos²θ?

• cos²θ + sin²θ = 1

• 1 + cot²θ = csc²θ

• tan²θ + 1 = sec²θ

• 1 - cos²θ = sin²θ

How can you simplify the expression tanθ * cosθ?

• sinθ

• 1

• cosθ

• tanθ

What identity can be used to simplify 1 - cos²θ?

• cos²θ

• tan²θ

• sin²θ

• 1

Which trigonometric function is equivalent to sinθ/cosθ?

• cscθ

• secθ

• cotθ

• tanθ

What is the solution for cos²θ = 1?

• θ = 0, π, 2π

• θ = π/2, 3π/2

• θ = π/4, 3π/4

• θ = π/3, 2π/3

Where does tanθ equal zero on the unit circle?

• θ = π/2, 3π/2

• θ = π/4, 3π/4

• θ = 0, π, 2π

• θ = π/3, 2π/3

What are the solutions for tanθ = -1 in the interval [0, 2π]?

• θ = 3π/4, 7π/4

• θ = π/4, 5π/4

• θ = π/2, 3π/2

• θ = 0, π