Trigonometric Functions and Inequalities

This video tutorial covers solving trigonometric equations and inequalities, focusing on tangent and sine functions. It explains the periodic nature of these functions and how to find solutions using inverse trigonometric functions. The video also demonstrates using graphing calculators to solve inequalities and model real-world scenarios with sinusoidal functions. It concludes with a discussion on inverse systems and provides links to additional resources.

What is the main topic of this video?

• Trigonometric identities

• Algebraic expressions

• Trigonometric equations and inequalities

• Calculus derivatives

What is the period of the tangent function?

• 2π

• π

• π/2

• 4π

How many solutions exist for the equation sin²(T) - 1 = 0?

• None

• Two

• Infinitely many

• One

Which function is likely the inverse of cosine?

• Arc cosine

• Sine

• Secant

• Tangent

What is the first step in using a graphing calculator to solve inequalities?

• Graph the function

• Adjust the window settings

• Reset the calculator

• Enter the inequality

What does the vertical translation in a sinusoidal function affect?

• Period

• Frequency

• Amplitude

• Midline

How often does point P touch the ground in the rocking horse scenario?

• Every 9 seconds

• Every 6 seconds

• Every 12 seconds

• Every 3 seconds

Which quadrant is the angle located if cosine is negative?

• First

• Second

• Fourth

• Third

What is the greatest interval length where f(x) is less than or equal to 5?

• 1

• 2

• 3

• 4