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Trigonometric Simplifications
English 10 leveled MCQs Free
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5 marks Long answer
Derive the expression for $L[\sin(3t) + \sin(t)]$.
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$L[\sin(3t) + \sin(t)] = rac{3}{s^2 + 9} + rac{1}{s^2 + 1}$
The full exam-length answer is in the app.
5 marks Long answer
Derive the expression for $L[\cos(5t) + \cos(t)]$.
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$L[\cos(5t) + \cos(t)] = rac{s}{s^2 + 25} + rac{s}{s^2 + 1}$
The full exam-length answer is in the app.
5 marks Long answer
Derive the expression for $L[\sin(9t) - \sin(t)]$.
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$L[\sin(9t) - \sin(t)] = rac{9}{s^2 + 81} - rac{1}{s^2 + 1}$
The full exam-length answer is in the app.
3 marks Medium answer
Simplify $2 \sin A \cos B$ using the sine addition formula.
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$2 \sin A \cos B = \sin(A+B) + \sin(A-B)$
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3 marks Medium answer
Simplify $2 \cos A \cos B$ using the cosine addition formula.
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$2 \cos A \cos B = \cos(A+B) + \cos(A-B)$
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3 marks Medium answer
Simplify $2 \cos A \sin B$ using the sine addition formula.
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$2 \cos A \sin B = \sin(A+B) - \sin(A-B)$
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1 marks Short answer
State the sine addition formula.
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$\sin(A+B) = \sin A \cos B + \cos A \sin B$
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1 marks Short answer
State the cosine addition formula.
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$\cos(A+B) = \cos A \cos B - \sin A \sin B$
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1 marks Short answer
What is the Laplace Transform of $\sin(at)$?
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$L[\sin(at)] = rac{a}{s^2 + a^2}$
The full exam-length answer is in the app.
1 marks Short answer
What is the Laplace Transform of $\cos(at)$?
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$L[\cos(at)] = rac{s}{s^2 + a^2}$
The full exam-length answer is in the app.
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