Joel Riggs
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Trigonometry Identities and Anti-Derivatives

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Joel Riggs
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  • Trigonometry Identities and Anti-Derivatives

    Question 1 of 9

    3

    What is the antiderivative of csc²(kx)?

    Select one of the following:

    • -(1/k)cot(kx)+c

    • (1/k)cot(kx)+c

    • -(1/k)tangent(kx)+c

    • (1/k)tangent(kx)+c

    • (1/k)sec(kx)+c

    • -(1/k)sec(kx)+c

    Explanation

    Question 2 of 9

    3

    What is the antiderivative of sec²(x)?

    Select one of the following:

    • (1/k)tangent(kx)+c

    • -(1/k)tangent(kx)+c

    • -(1/k)csc(kx)+c

    • (1/k)csc(kx)+c

    • -(1/k)sin(kx)+c

    • (1/k)sin(kx)+c

    Explanation

    Question 3 of 9

    3

    Which is an identity of sin²(x)?

    Select one of the following:

    • (1-cos(2x))*(1/2)

    • (1+cos(2x))*(1/2)

    • cos(x)

    • sin(x)cos(y)+cos(x)sin(y)

    • 2tan(x)/(1-tan²(x))

    • 2sin((x+y)/2)sin((x-y)/2)

    Explanation

    Question 4 of 9

    3

    Which of the following are identities of tan²(x)?

    Select one of the following:

    • (1-cos(2x))/(1+cos(2x))

    • (1+cos(2x))/(1-cos(2x))

    • [tangent(x)+tangent(y)]/[1-tangent(x)tangent(y)]

    • (1/2)*[cos(x+y)+cos(x-y)]

    Explanation

    Question 5 of 9

    3

    What is the antiderivative of csc(kx)cot(kx)?

    Select one of the following:

    • -(1/k)csc(kx)+c

    • (1/k)csc(kx)+c

    • (1/k)[sin(kx)/cos(kx)]+c

    • -(1/k)[sin(kx)/cos(kx)]+c

    Explanation

    Question 6 of 9

    3

    What is the antiderivative of sec(kx)tangent(kx)?

    Select one of the following:

    • (1/k)sec(kx)+c

    • -(1/k)sec(kx)+c

    • (1/k)csc(kx)+c

    • -(1/k)csc(kx)+c

    Explanation

    Question 7 of 9

    3

    What is the anti-derivative of sin(kx)

    Select one of the following:

    • -(1/k)cos(kx)+c

    • (1/k)cos(kx)+c

    • (1/k)sin(kx)+c

    • (1/k)csc(kx)+c

    Explanation

    Question 8 of 9

    3

    Which of the following are identities of cos(2x)?

    Select one or more of the following:

    • cos²(x)-sin²(x)

    • 1-2sin²(x)

    • 2cos²(x)-1

    • 2cos²(x)+1

    • (1-cos(2x))*(1/2)

    • csc²(x)

    • cos(x)cos(y)+sin(x)sin(y)

    • (1-cos(2x))/(1+cos(2x))

    • 2/(cot(x)-tangent(x))

    Explanation

    Question 9 of 9

    3

    What is the anti-derivative of cos(kx)

    Select one of the following:

    • (1/k)sin(kx)+c

    • -(1/k)sin(kx)+c

    Explanation