MathDB

1

Part of 2019 Auckland Mathematical Olympiad

Problems(2)

<ACB=? <BAC=20,<CAD=60, <ADB=<50, <BDC =10 (2019 Auckland MO J1)

Source:

12/31/2020
Given a convex quadrilateral ABCDABCD in which ∠BAC=20o\angle BAC = 20^o, ∠CAD=60o\angle CAD = 60^o, ∠ADB=50o\angle ADB = 50^o , and ∠BDC=10o\angle BDC = 10^o. Find ∠ACB\angle ACB.
geometryangles
f(sin x) = sin(17x) if f(cos x) = cos(17x) (2019 Auckland MO S1)

Source:

11/15/2021
Function ff satisfies the equation f(cos⁡x)=cos⁡(17x)f(\cos x) = \cos (17x). Prove that it also satisfies the equation f(sin⁡x)=sin⁡(17x)f(\sin x) = \sin (17x).
trigonometryalgebra