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# Cos is 1/13 What is sin? Answered in terms of an integer w/ square roots intact and unsolved.?

How do I find the sin with the cos of 1/13 available to me? It s for math homework and the course actually shows me what the answer is, but I don t understand how it got to it because it just lumps the entire solving into "simplify". Attached is the example it gives.

Couldn't attach file or picture, but an example of:

Cos 1/10

Came to 3 [square root of]11 /10.

Where did the 3 and 11 come from?!?

### 2 Answers

- MathmomLv 72 years agoFavorite Answer
For cosθ = 1/10

sin²θ + cos²θ = 1 ----> you should know this

sin²θ = 1 − cos²θ

sin²θ = 1 − (1/10)²

sin²θ = 1 − 1/100

sin²θ = 99/100

sinθ = ± √(99/100)

sinθ = ± √99/√100

sinθ = ± 3√11/10

Note 1: √99 = √(9*11) = √9√11 = 3√11 ----> this is where 3 and 11 come from

Note 2: without knowing anything about the angle θ, it's not possible to determine if sinθ is positive or negative. If you have not yet learned anything about sine and cosine for larger angles (greater than 90 degrees), then θ is most likely an acute angle, so we can use positive value for sinθ

For cosθ = 1/13

sin²θ + cos²θ = 1

sin²θ = 1 − cos²θ

sin²θ = 1 − (1/13)²

sin²θ = 1 − 1/169

sin²θ = 168/169

sinθ = ± √(168/169)

sinθ = ± √168/√169

sinθ = ± 2√42/13

Very detailed! Thank you!