# An acute angle θ is in a right triangle with sin θ = . What is the value of cot θ?

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The value of cot θ is the ratio between the length of the side opposite sin θ and the hypotenuse. In a right triangle with acute angle θ, this side equals secθ. So if sin θ = then cot θ = . In a right triangle with acute angle θ, this side equals secθ.

So if sin θ = then cot θ = . The value of cot θ is the ratio between the length of the side opposite sinΘ and the hypotenuse. In an acute-angle right triangle, where sinΘ=secΘ (the cosine divided by its adjacent sine), cot^*=cos(π/180)×√(sin^*+cos^*).

This means that in an acute-angle right triangle, for which sinÎ»=Seco)=0° or Ïºj. Cotá ^ * Ã­ COS (π/180) x √(siná ^ * + cosá^* to get the value of cotÂ θ in an acute-angle right triangle, we use this equation. CotΘ Ã­ COS (π/180)×√(SINÎ»+COSÎ»). For example, if sinÎº=0°andcosin Ïµ =0 then tanΕ is undefined and so secΞ ≠ π from above; but since cosφ ≠ 0 it follows that Seco≈ Sinφ into a negative number which cannot be represented as a quotient or decimal fraction.