Understanding Sine and Arcsine Functions

The video tutorial explains the concept of sine and arcsine using the unit circle and triangles. It starts with calculating the sine of pi/4, demonstrating the use of the unit circle and 45-45-90 triangle properties. The tutorial then introduces the arcsine function, explaining its inverse relationship with sine and the need to restrict its range for it to be a valid function. Finally, it covers the calculation of arcsine for negative values, using a 30-60-90 triangle and confirming results with a calculator.

What is the sine of pi over 4?

• 1

• 0

• Square root of 3 over 2

• Square root of 2 over 2

In a 45-45-90 triangle, if the hypotenuse is 1, what is the length of each leg?

• Square root of 2 over 2

• 1/2

• Square root of 2

• 1

What does the arcsine function represent?

• The tangent of an angle

• The cotangent of an angle

• The angle whose sine is a given value

• The cosine of an angle

What is the inverse sine of the square root of 2 over 2?

• Pi over 4

• Pi over 2

• 2 Pi

• Pi

Why must the range of the inverse sine function be restricted?

• To ensure it is a valid function

• To make it easier to calculate

• To match the range of cosine

• To avoid negative values

What is the restricted range for the arcsine function?

• Minus Pi to Pi

• Minus Pi over 2 to Pi over 2

• 0 to 2 Pi

• 0 to Pi

What is the domain of the arcsine function?

• Less than -1

• Greater than 1

• Between -1 and 1

• All real numbers

In which quadrants is the arcsine function defined?

• First and fourth

• Third and fourth

• First and second

• Second and third

What is the arcsine of minus square root of 3 over 2 in radians?

• Minus Pi over 3

• Minus Pi over 6

• Minus Pi over 2

• Minus Pi

In a 30-60-90 triangle, what is the length of the side opposite the 60-degree angle if the hypotenuse is 1?

• Square root of 2 over 2

• 1

• 1/2

• Square root of 3 over 2