Trigonometry

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Write the trigonometric expression as an algebraic expression.
1.) SIN(ARCSIN X+ARCCOS X)
ANSWER: 1
2.) SIN(ARCTAN 2X-ARCCOS X)
ANSWER: 2x²-SquareRoot of 1-x²/Square
Root of 4x²+1.

  • Trigonometry -

    1.) Apply the following method you used in #2! You should notably understand this already! Goodness grief!

    2.) let A = arctan x
    let B = arccos x

    then we are looking for
    sin(A + B) .

    now,
    tan A = x ,
    sin A = x/√(x^2+1)
    cos A = 1/√(x^2+1) ... create a right triangle where the opposite side is x, and the adjacent side is 1 ... the hypotenuse is √(x^2+1)

    cos B = x
    sin B = √(1 - x^2)


    meanwhile
    sin(A + B)
    = sin A cos B + cos A sin B
    = x/√(x^2+1) * x + 1/√(x^2+1) * √(1 - x^2)
    = [x^2 + √(1 - x^2)] / (x^2 + 1) .

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