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Math Help - Various Trig Problems

  1. #1
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    Various Trig Problems

    1. Find the x and y-intercepts of X / x-x-6
    2. Find the vertical asymptote of (x-8)(x+4) / x-1
    3. Find the slant asymptote of x+2x-3 / x-5
    4. Assume that θ is an acute angle in a right triangle. Evaluate the indicated trigonometric function

    tan θ =1/3; csc θ

    5. Phase shift of -2+2sin(3x+pi/2)
    6. Exact value of arcsin(-(sqrt3)/2)
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  2. #2
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    Re: Various Trig Problems

    Have you read your textbook or tried any of these problems?

    To find the x-intercept, set x=0 and solve for y.
    To find the y-intercept, set y=0 and solve for x (you may get multiple solutions).
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  3. #3
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    Re: Various Trig Problems

    Q 5. Compare The expression with the standard from i.e., f(x) = A sin ( Bx + C ) + D the phase shift is given by C. In this case the phase shift is pi/2
    Q 6. arcsin(-(sqrt3)/2) that means we want to find that angle for which sin has the value -(-(sqrt3)/2).
    We have learnt that Sinθ = √3/2 for θ= π/3 and also trigonometric ratio sine is negative in 3rd and 4th Quadrant.
    Therefore Sinθ = - √3/2 for θ = π+ π/3= 4π/3 and 2π- π/3= 5π/3.
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  4. #4
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    Re: Various Trig Problems

    Hello, whittwhitt!

    3. Find the slant asymptote of: . y \:=\:\frac{x^2+2x-3}{x-5}

    Long division: . \frac{x^2+2x-3}{x-5} \:=\:x+7 + \frac{32}{x-5}

    As x\to\infty,\;\frac{32}{x-5} \to 0.

    Therefore, the slant asymptote is: . y \:=\:x+7




    \text{4. Assume that }\theta\text{ is an acute angle in a right triangle and }\tan\theta = \tfrac{1}{3}
    \text{Evaluate: }\:\csc\theta

    We have: . \tan\theta \:=\:\frac{1}{3} \:=\:\frac{opp}{adj}

    \theta is in a right triangle with: opp = 1,\;adj=3.
    Pythagorus tells us that: hyp = \sqrt{10}.

    Therefore: . \csc\theta \:=\:\frac{hyp}{opp} \:=\:\frac{\sqrt{10}}{1} \:=\:\sqrt{10}
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