Given: θ ∈ [ π / 2 , π ] and tan ⁡ θ = 1 / 3.Find sin ⁡ θ and cos ⁡ θ (but to find the angle is not needed)

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Given:   θ  ∈  [  π      /    2  ,  π  ] and   tan  ⁡  θ  =  1      /    3.Find   sin  ⁡  θ and   cos  ⁡  θ (but to find the angle is not needed)

pelvogp · Accepted Answer

Given:   θ  ∈  [  π      /    2  ,  π  ] and   tan  ⁡  θ  =  1      /    3.Find   sin  ⁡  θ and   cos  ⁡  θ (but to find theangle is not needed)  tan  ⁡  θ  =  1      /    3  ⇒  h  y  p  =      9    +    1    =      10    sin  ⁡  θ  =  1      /        10    cos  ⁡  θ  =  3      /        10

traucaderx7 · Accepted Answer

we have two solutions to the question  tan  ⁡  θ  =  1      /    3clearly we have a right angle triangle withp=1, b=3thus   h  =            3              2              +      1          2        =  ±      10  so either   cos  ⁡  θ  =  3      /        10    ,  sin  ⁡  θ  =  1      /        10  or   cos  ⁡  θ  =  −  3      /        10    ,  sin  ⁡  θ  =  −  1      /        10  if n is specified then   θ and thus exact solution can be determined

Given: theta in [pi /2, pi ] and tan theta = 1/3. Find sin theta and cos theta (but to find theangle is not needed)

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