Directions: Using the digits 0 to 9, at most one time, fill in the blanks to create sine and cosine functions with the given periods in degrees.

### Hint

Which function has more possible answers? Therefore, where is the smartest place to start?

Many numbers for b will result in a period with last digit 0, but you can only use 0 one time, so you can not have two periods that have the last digit 0. What insight might this give you about what numbers to start with?

### Answer

Option 1 for cosine function y=cos 4x yields two possible solutions:

y=cos 4x with a period of 90° & y=sin 5/3x with a period of 216°

y=cos 4x with a period of 90° & y=sin 8/7x with a period of 315°

The related option for the cosine function y=cos 9x gives us:

y=cos 9x with a period of 40° & y=sin 5/3x with a period of 216°

y=cos 9x with a period of 40° & y=sin 8/7x with a period of 315°

For the cosine function y=cos 5x, we have the following solutions:

y=cos 5x with a period of 72° & y=sin 6/3x with a period of 180°

y=cos 5x with a period of 72° & y=sin 9/4x with a period of 160°

y=cos 5x with a period of 72° & y=sin 3/8x with a period of 960°

y=cos 5x with a period of 72° & y=sin 4/9x with a period of 810°

Finally, for the cosine function y=cos 8x, we can find:

y=cos 8x with a period of 45° & y=sin 3/6x with a period of 720°

y=cos 8x with a period of 45° & y=sin 9/3x with a period of 120°

Source: Kate Nerdypoo