Ask Uncle Colin: Trigonometric inverses and picking the correct quadrant | Colin

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions — and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can.

Dear Uncle Colin,

When I have an angle in the second quadrant, I can find it just fine using $\cos^{-1}$ – but using $\sin^{-1}$ or $\tan^{-1}$ gives me an angle in the fourth quadrant. I don’t understand why this is!

— I Need Verbose Explanations; Radians Seem Excellent

Hi, INVERSE, and thanks for your message!

The short answer is,…

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