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    Trigonometry questions of identity

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    1. Express in equivalent form: log x + log 1 - 6 log (y + 4)

    2. Points (4, -7) and (6, 3) are endpoints of the diameter of a circle./
    (a) What is the exact length of the diameter?
    (b) What is the center of the circle?
    (c) What is the equation of the circle?

    3. Given y = 9 sin(8x - p), state the
    (a) period
    (b) phase shift

    4. Solve the trigonometric equation (sin x)(2cos x − 1) = 0 in the interval [0, 360°).
    (a) Find the exact value of arccos sin( 3π/ 2 )
    (b) Find the exact value of arcsin sin( 2π/3 )

    5. Solve. ( x+13/x+6 ) + ( 84/ x^2-36) = 0

    6. Suppose that sin q = 5/13 and that q is a Quadrant II angle.
    (a) Find the exact value of cos ϴ
    (b) Find the exact value of sin 2ϴ.

    7. Prove the identity 1 - (sin x - cos x)2 = sin 2x

    © BrainMass Inc. brainmass.com December 24, 2021, 11:52 pm ad1c9bdddf
    https://brainmass.com/math/functional-analysis/trigonometry-questions-identity-612173

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    SOLUTION This solution is FREE courtesy of BrainMass!

    1. Express in equivalent form: log x + log 1 - 6 log (y + 4)
    Solution:

    Answer:

    2. Points (4, -7) and (6, 3) are endpoints of the diameter of a circle.
    (a) What is the exact length of the diameter?
    Solution:
    Diameter

    Answer:
    (b) What is the center of the circle?
    Solution:
    Center =
    Answer: (5,-2)
    (c) What is the equation of the circle?
    Solution:
    Radius = /2 =

    Equation of circle will be

    3. Given y = 9 sin(8x - π), state the
    (a) period

    Solution:

    Period = 2π/|B| = 2π/8 = π/4

    Answer: π/4

    (b) phase shift

    Solution:

    Phase shift = C/B = π/8

    Answer: π/8

    4. Solve the trigonometric equation (sin x)(2cos x − 1) = 0 in the interval [0, 360°).

    Solution:

    (sin x)(2cos x − 1) = 0
    Sinx = 0 or 2cosx-1 =0
    Sinx = 0 or cosx = ½

    When sinx = 0
    x = 0, 180°, 360°

    When cosx = ½
    x = 60°, 300°

    Answer: x = 0°, 60°, 180°, 300°, 360°

    (a) Find the exact value of arccos sin( 3π/ 2 )

    Solution:
    arccos sin( 3π/ 2 ) = arcos(-1) = π

    (b) Find the exact value of arcsin sin( 2π/3 )

    Solution:

    arcsin (sin( 2π/3 )) = 2π/3

    Answer: 2π/3

    5. Solve. ( x+13/x+6 ) + ( 84/ x^2-36) = 0

    Solution:

    The only solution is x =-1 as given equation is not defined at x = -6.

    Answer: x = -1

    6. Suppose that sin q = 5/13 and that q is a Quadrant II angle.
    (a) Find the exact value of cos q

    Solution:

    cosq =

    (b) Find the exact value of sin 2q.

    Solution:

    sin 2q = 2sinqcosq = 2*

    Answer:

    7. Prove the identity 1 - (sin x - cos x)2 = sin 2x
    Solution:

    Hence proved

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 11:52 pm ad1c9bdddf>
    https://brainmass.com/math/functional-analysis/trigonometry-questions-identity-612173

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