Quick questions on Trigonometric and rationalising substitutions in HSC Mathematics Extension 2: substitutions for square-root integrands, completing the square, and the t = tan(x/2) substitution

Q: What is sign of the square root?

sqrt(a^2cos^2θ) = a|cosθ|. Choose the range of θ so cosine is non-negative, otherwise a sign error creeps in.

1short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is sign of the square root?

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\sqrt{a^2\cos^2\theta} = a|\cos\theta|

. Choose the range of

\theta

so cosine is non-negative, otherwise a sign error creeps in.

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