# Rational Sine and Cosine

Pro Problems > Math > Logic > Proofs## Rational Sine and Cosine

There are infinitely many angles θ between 0º and 90º for which both sin θ and cos θ are rational numbers. Prove this statement.

Hint: Here are some examples:

sin θ

cos θ

3

5

4

5

5

13

12

13

7

25

24

25

9

41

40

41

Presentation mode

Problem by Mr. Twitchell

## Solution

In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.Assign this problem

Click here to assign this problem to your students.## Similar Problems

### Ones Place Proof

Four consecutive integers are multiplied together. Determine, with proof, which digits could be in the ones place of the resulting product.

### Cubes and Nine

Prove that all perfect cubes are either a multiple of 9, one more than a multiple of 9, or one less than a multiple of 9.

### Product of Digits

Prove that there is no two digit number which is equal to the product of its digits.

### Squares Mod Four

Prove that all perfect squares are either a multiple of 4, or one more than a multiple of 4.

# Ask Professor Puzzler

Do you have a question you would like to ask Professor Puzzler? Click here to ask your question!**Get a**

*FREE*Pro-Membership!Educators can get a free membership simply by sharing an original lesson plan on our

*Articles for Educators*page!

Like us on Facebook to get updates about new resources