Trigonometric Functions and Their Properties

The video tutorial explains solving trigonometric equations by expanding the domain to find all possible solutions. It begins with setting up the problem and identifying initial solutions. The instructor then discusses frequency changes in trigonometric functions and how these affect the number of solutions. The concept is applied to both tangent and sine functions, demonstrating how to adjust the domain to capture all solutions within a specified range.

What is the period of the tan function?

• 270°

• 90°

• 180°

• 360°

How does the frequency of tan(2x) compare to tan(x)?

• Same frequency

• More frequent

• Less frequent

• No frequency

What happens to the domain when solving for 2x instead of x?

• It is tripled

• It remains the same

• It is doubled

• It is halved

How many solutions are there for tan(2x) in the domain 0 to 720?

• Four

• Two

• Five

• Three

What is the first solution for sin(x - 250) = √3/2?

• 60°

• 90°

• 45°

• 30°

Why is 120° not a solution for sin(x - 250) = √3/2 in the modified domain?

• It is a duplicate solution

• It is not a valid angle

• It is a negative angle

• It is outside the domain

What is the period of the sine function?

• 90°

• 270°

• 180°

• 360°

How do you find additional solutions for sin(x - 250) = √3/2?

• Subtract 90°

• Add 90°

• Subtract 360°

• Add 360°

What is the modified domain for x - 250 when solving sin(x - 250) = √3/2?

• 0 to 720

• -360 to 360

• 0 to 360

• -250 to 110

What is the final step to find x from x - 250?

• Add 250

• Subtract 250

• Divide by 2

• Multiply by 2