Quick questions on Essential trigonometric identities: Pythagorean, ratio, complementary and double angle

2short 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 a proof, stage by stage?

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Here is the 2022 HSC proof

\dfrac{1 - \cos 2\theta}{\sin 2\theta} = \tan\theta

run as a chain of transformations. Read it top to bottom; each box is the line above with exactly one identity applied.

What is sign errors from the quadrant?

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When given a value of

\sin \theta

and a quadrant, the sign of

\cos \theta

(or

\tan \theta

) depends on the quadrant: positive in Q1; sine positive, cosine negative in Q2; both negative in Q3; cosine positive, sine negative in Q4.

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