Find the remaining side of the right angle triangle and the six trigonometric functions as functions of x : height (opp)= `sqrt(2x^(2)+8)`, hypotenuse = x-2. What is theta?
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The height of the right angle triangle is `sqrt(2x^2+ 8)` and the hypotenuse is x - 2. If the base is B,
`B^2 + (sqrt(x^2 + 8x))^2 = (x - 2)^2`
=> `B^2 + x^2 + 8x = x^2 - 4x + 4`
=> B^2 + 8x = 4 - 12x
=> B = `sqrt(4 - 12x)`
`theta = cos^-1(sqrt(4 - 12x)/(x - 2))`
`sin theta = sqrt(2x^2 + 8)/(x - 2)`
`tan theta = sqrt(2x^2 + 8)/sqrt(4 - 12x)`
The inverse of sine, cosine and tangent of the angle gives the cosec, sec and cotangent of the angle.
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