Standard +0.3 This requires expanding cos(x + 30°) using the compound angle formula, rearranging to form a linear equation in sin x and cos x, then solving using tan x substitution or dividing through. It's a standard compound angle equation with straightforward algebraic manipulation, slightly above average due to the multiple-step process and finding all solutions in the given interval, but still a routine P3 exercise.
Use \(\cos(A + B)\) formula to obtain an equation in \(\cos x\) and \(\sin x\)
M1
Use trig formula to obtain an equation in \(\tan x\) (or \(\cos x\) or \(\sin x\))
M1
Obtain \(\tan x = \sqrt{3} - 4\), or equivalent (or find \(\cos x\) or \(\sin x\))
A1
Obtain answer \(x = -66.2°\)
A1
Obtain answer \(x = 113.8°\) and no others in the given interval
A1
[Ignore answers outside the given interval. Treat answers in radians as a misread \((-1.16, 1.99)\).]
Total: 5 marks
[The other solution methods are via \(\cos x = \pm1/\sqrt{(1 + (\sqrt{3} - 4)^2)}\) and \(\sin x = \pm(\sqrt{3} - 4)/\sqrt{(1 + (\sqrt{3} - 4)^2)}\) .]
Use $\cos(A + B)$ formula to obtain an equation in $\cos x$ and $\sin x$ | M1 |
Use trig formula to obtain an equation in $\tan x$ (or $\cos x$ or $\sin x$) | M1 |
Obtain $\tan x = \sqrt{3} - 4$, or equivalent (or find $\cos x$ or $\sin x$) | A1 |
Obtain answer $x = -66.2°$ | A1 |
Obtain answer $x = 113.8°$ and no others in the given interval | A1 |
[Ignore answers outside the given interval. Treat answers in radians as a misread $(-1.16, 1.99)$.] | Total: 5 marks |
[The other solution methods are via $\cos x = \pm1/\sqrt{(1 + (\sqrt{3} - 4)^2)}$ and $\sin x = \pm(\sqrt{3} - 4)/\sqrt{(1 + (\sqrt{3} - 4)^2)}$ .]
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