TMUA Official 2017 Paper 2 · Question 4

The following question appeared in an examination:

Given that $\tan x=\sqrt3$ , find the possible values of $\sin2x$ .

A student gave the following answer:

$\tan x=\sqrt3$ so $x=60^\circ$ and $2x=120^\circ$ , therefore $\sin2x=\dfrac{\sqrt3}2$ .

Which one of the following statements is correct?

\frac{\sqrt3}2

is the only possible value, and this is fully supported by the reasoning given in the student's answer.

\frac{\sqrt3}2

is the only possible value, but the reasoning given should consider other possible values of

x

for which

\tan x=\sqrt3

\frac{\sqrt3}2

is the only possible value, but the reasoning given should consider other possible values of

x

for which

\sin2x=\frac{\sqrt3}2

\frac{\sqrt3}2

is not the only possible value because the reasoning given should have considered other possible values of

x

for which

\tan x=\sqrt3

\frac{\sqrt3}2

is not the only possible value because the reasoning given should have considered other possible values of

x

for which

\sin2x=\frac{\sqrt3}2

examday