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Daniel J Smith Custom TMUA Set A Paper 1 · Q13

Paper 1TrigonometryFunctions & graphsAlgebra

Let cc be a real constant.

Consider the equation

∣sin⁡x∣+∣cos⁡x∣=c|\sin x|+|\cos x|=c

for 0≤x<2π0\leq x<2\pi

Which of the following gives the number of distinct solutions as a function of cc?

AIf 0<c<10<c<1, there are 88 solutions; if 1<c<21<c<\sqrt2 there are 44 solutions; if c=1c=1 or c=2c=\sqrt2 there are 22 solutions; otherwise there are 00 solutions
BIf 0<c<10<c<1, there are 00 solutions; if c=1c=1 there are 44 solutions; if 1<c<21<c<\sqrt2 there are 88 solutions; if c=2c=\sqrt2 there are 44 solutions; otherwise there are 00 solutions
CIf 0<c<10<c<1, there are 00 solutions; if c=1c=1 there are 22 solutions; if 1<c<21<c<\sqrt2 there are 44 solutions; if c=2c=\sqrt2 there are 88 solutions; otherwise there are 00 solutions
DIf 0<c<10<c<1, there are 44 solutions; if c=1c=1 there are 88 solutions; if 1<c<21<c<\sqrt2 there are 44 solutions; if c=2c=\sqrt2 there are 22 solutions; otherwise there are 00 solutions
EIf 0<c<10<c<1, there are 00 solutions; if 1≤c≤21\leq c\leq\sqrt2 there are 88 solutions; otherwise there are 00 solutions
FIf 0<c<20<c<\sqrt2 there are 88 solutions; if c=2c=\sqrt2 there are 44 solutions; if c>2c>\sqrt2 there are 00 solutions

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