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Math Help - Trig Graphs and Equations

  1. #1
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    Exclamation Trig Graphs and Equations

    Can anyone please provide the answers to these questions as this is due tomoroow. Any help would be much appreciated thanks.


    (1) Solve:
    (a) 2sinx = 0.2, 0o ≤ x ≤ 360o
    (b) sinx + 3 = 3.5, 0 ≤ x ≤ 2π
    (c) 3sin2x = 0.8, 0o ≤ x ≤ 360o
    (d) sin(x – 90o) = 0.3, -180o ≤ x ≤ 180o
    (e) 2sinx + 3 = 2, 0 ≤ x ≤ 2π.

    (2) Solve the following trigonometric equations:
    (a)tan(theta) = -1.3, 0(degrees)
    (b) cos(theta) +3 = 3.1
    (c)14sin(theta) = 10

    (3) The fans on a windmill rotate at a constant speed.
    P is the point at the end of the fan.
    The height, h m, of P above the ground
    at time t seconds is given by the equation:
    h = 24 + 15sin t , t is measured in radians.
    (a) How long does it take the point P to move from the top to the bottom of the arc?
    (b) What proportion of a cycle is the point P above 30 metres?
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  2. #2
    MHF Contributor
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    Are calculators allowed?

    For most of 1) and 2), you need to solve the equations so that you get "trig function (x) = A", where trig function is sine, cosine, whatever and then you use the trig inverse to solve for the angle. On your calculator, it looks like \sin^{-1}(x) or something similar.
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  3. #3
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    Yes we are allowed calculators.
    Would you be able to please show me one of the questions so i get the idea and can do the rest?
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  4. #4
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    Sure.

    1(a). 2sinx = .2
    sinx = .1

    x = \sin^{-1}(.1)

    In words...
    x = the sine inverse of .1.

    I don't have a calculator handy. Do you see how it's done?
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  5. #5
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    Response to Brownhash

    Trig Graphs and Equations
    Can anyone please provide the answers to these questions as this is due tomoroow. Any help would be much appreciated thanks.


    (1) Solve:
    (a) 2sinx = 0.2, 0o ≤ x ≤ 360o
    (b) sinx + 3 = 3.5, 0 ≤ x ≤ 2π
    (c) 3sin2x = 0.8, 0o ≤ x ≤ 360o
    (d) sin(x 90o) = 0.3, -180o ≤ x ≤ 180o
    (e) 2sinx + 3 = 2, 0 ≤ x ≤ 2π.

    (2) Solve the following trigonometric equations:
    (a)tan(theta) = -1.3, 0(degrees)
    (b) cos(theta) +3 = 3.1
    (c)14sin(theta) = 10

    (3) The fans on a windmill rotate at a constant speed.
    P is the point at the end of the fan.
    The height, h m, of P above the ground
    at time t seconds is given by the equation:
    h = 24 + 15sin t , t is measured in radians.
    (a) How long does it take the point P to move from the top to the bottom of the arc?
    (b) What proportion of a cycle is the point P above 30 metres?

    Response by Math genius
    One way to solve question one is the use of general formulars:
    The one for sin x = a is x = 180n +(-1)^n x p where p = sin-1 a
    The one for cos x = a is x = 360n + p where p = cos-1 a
    The one for tan x = a is x = 180n + p where p = sin-1 a
    n = 0,1,2,3,.... untill all angles in range are exhausted... try this
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