Trigonometric Functions and Their Properties

The video tutorial covers the tangent function's domain, periodicity, and range, using graphs and the unit circle. It explains angles where tangent values exceed one and cosine values are negative. The tutorial also calculates rotation angles for clock hands and demonstrates graph transformations of quadratic functions.

What is the domain of the tangent function?

• All real numbers

• All real numbers except multiples of Pi

• All real numbers except even multiples of Pi

• All real numbers except odd multiples of Pi/2

Why is the tangent function undefined at Pi/2?

• Because the tangent is zero

• Because both sine and cosine are zero

• Because the cosine is zero

• Because the sine is zero

What are the theta intercepts of the tangent graph?

• Multiples of Pi

• Multiples of Pi/2

• Multiples of 3Pi

• Multiples of 2Pi

Why is the tangent of multiples of Pi equal to zero?

• Because the sine is zero

• Because the cosine is zero

• Because both sine and cosine are zero

• Because the tangent is undefined

Which of the following is true about the tangent function?

• Its period is 2Pi

• Its range is all real numbers

• Its domain is all real numbers

• It is not periodic

What is the period of the tangent function?

• 4Pi

• 3Pi

• 2Pi

• Pi

Where on the unit circle is the tangent greater than one?

• Between Pi/4 and Pi/2

• Between 0 and Pi/4

• Between Pi/2 and 3Pi/4

• Between 3Pi/4 and Pi

At which angle is the tangent of the unit circle undefined?

• Pi/2

• Pi/4

• 3Pi/4

• Pi

What is the slope of a line through the origin and point P on the unit circle?

• Undefined

• 1/2

• 1

• 2

When is the cosine less than zero on the unit circle?

• In the second quadrant

• In the third quadrant

• In the fourth quadrant

• In the first quadrant