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.

Update:

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

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  • 2 years ago
    Favorite 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

    • Kurt2 years agoReport

      Very detailed! Thank you!

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  • Como
    Lv 7
    2 years ago

    y² = 13² - 1²

    y² = 168

    y = 2 √42

    sin Ө = 2 √42 / 13

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