Sine and Cosine Functions Concepts

The video tutorial explores the sine and cosine functions, highlighting their limitations on calculators, which typically provide results only between 0 and 90 degrees. It explains the graphical representation of these functions, known as sine waves, and discusses their properties, including symmetry. The tutorial also covers advanced calculations for angles beyond 90 degrees and provides historical context on how these calculations were performed before modern calculators, using tools like the slide rule.

Why do calculators typically not provide sine and cosine values for angles greater than 90 degrees?

• The values are not defined beyond 90 degrees.

• The calculator's display cannot show such values.

• The values become negative beyond 90 degrees.

• They are not programmed to handle angles beyond 90 degrees.

What is the maximum value that sine and cosine functions can reach on a graph?

• 2

• 0

• 1

• -1

How does the sine wave start on a graph?

• At 90 degrees

• At -1

• At 1

• At 0

What is the starting point of the cosine wave on a graph?

• At 0

• At 1

• At -1

• At 90 degrees

What is a major limitation of calculators when dealing with sine and cosine values?

• They provide incorrect values for angles greater than 180 degrees.

• They cannot handle negative angles.

• They cannot calculate values for angles less than 0 degrees.

• They only provide values for angles up to 90 degrees.

How can you determine the sine value for an angle greater than 90 degrees?

• By subtracting 90 from the sine value of the angle.

• By using a calculator's advanced functions.

• By adding 90 to the sine value of the angle.

• By using the symmetry of the sine wave.

If the sine of an angle is 0.7, what is the angle if it is greater than 90 degrees?

• 136 degrees

• 90 degrees

• 44 degrees

• 180 degrees

Before calculators, what tool was used to calculate sine and cosine values?

• Compass

• Protractor

• Abacus

• Slide rule