Mathematics · Oct / Nov 2020 · Paper 31 · Question 1
YMA01
As printed in the paper
The question as text
1. Solve, for 0 x < 360°, the equation 2 cos 2 x = 7 cos x giving your solutions to one decimal place. (Solutions based entirely on graphical or numerical methods are not acceptable.) (5)
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Show the answer and mark scheme
2 2cos
2
x
−
1
=
7cos
x
1
4cos
2
x
−
7cos
x
−
2
=
0
⇒
cos
x
= −
4
1
⇒
x
=
arccos
−
=
104.5 , 255.5
°
°
4
2
M1
Attempts to use
cos2
x
= ±
2cos
x
± to form a quadratic equation in cos x
1
If the other two forms are attempted there must be some attempt to use
sin
2
x
+
cos
2
x
= to form a
1
quadratic equation in cos x
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