Trigonometric Equations and Functions

This video tutorial covers solving trigonometric equations using inverse functions and the unit circle. It begins with an introduction to the topic, followed by detailed examples involving sine, cosine, and tangent. The tutorial also includes factoring techniques and advanced problem-solving strategies. Students are guided through each example step-by-step, with emphasis on understanding the unit circle and quadrant rules.

Which quadrant has all trigonometric functions positive?

• Fourth quadrant

• First quadrant

• Second quadrant

• Third quadrant

What is the sine of an angle in the second quadrant?

• Positive

• Negative

• Zero

• Undefined

When solving the equation 2sin(θ) = 1, what is the value of θ in the first quadrant?

• π/3

• π/4

• π/6

• π/2

In the equation tan(θ) = √3, which family of angles should be considered?

• π/4 family

• π/6 family

• π/2 family

• π/3 family

What is the cosine of an angle in the fourth quadrant?

• Negative

• Positive

• Zero

• Undefined

How do you solve the equation 2cos(θ) = 1 for θ?

• θ = π/3 and 5π/3

• θ = π/4 and 7π/4

• θ = π/6 and 11π/6

• θ = π/2 and 3π/2

What is the result of factoring the expression 2x^2 - x - 1?

• (2x + 1)(x - 1)

• (x + 1)(2x - 1)

• (2x - 1)(x + 1)

• (x - 1)(2x + 1)

In the equation sin(θ) = 0, what are the possible values of θ?

• π/4 and 7π/4

• π/2 and 3π/2

• π/3 and 5π/3

• 0 and π

What is the value of θ when cos(θ) = 1?

• 0

• π/2

• π

• 3π/2

If sin(θ) = 3, what is the solution for θ?

• No solution

• θ = π

• θ = π/2

• θ = 0