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How do you find cos θ sec θ cot θ and the hypotenuse of the right triangle with a known sin θ equals 2 over x?
Wiki User
∙ 11y ago
By using the sine ratio, you know two sides of the right triangle (the opposite and hypotenuse) and so can work out the third side (adjacent) using Pythagoras (opposite2 + adjacent2 = hypotenuse2).
You can then use the trigonometric ratios to calculate cos θ, sec θ, cot θ, and the hypotenuse you already have.
Sin θ = opposite/hypotenuse = 2/x
⇒ opposite = 2, hypotenuse = x, and adjacent = √(x2 - 4)
Thus:
cos θ = adjacent/hypotenuse = √(x2 - 4)/x
sec θ = 1/cos θ = hypotenuse/adjacent = x/√(x2 - 4)
cot θ = 1/tan θ = adjacent/opposite = √(x2 - 4)/2
Hypotenuse = x.
Wiki User
∙ 11y ago
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