| Date | May 2015 | Marks available | 6 | Reference code | 15M.1.hl.TZ2.3 |
| Level | HL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 3 | Adapted from | N/A |
Question
Find all solutions to the equation \(\tan x + \tan 2x = 0\) where \(0^\circ \le x < 360^\circ\).
Markscheme
\(\tan x + \tan 2x = 0\)
\(\tan x + \frac{{2\tan x}}{{1 - {{\tan }^2}x}} = 0\) M1
\(\tan x - {\tan ^3}x + 2\tan x = 0\) A1
\(\tan x(3 - {\tan ^2}x) = 0\) (M1)
\(\tan x = 0 \Rightarrow x = 0,{\text{ }}x = 180^\circ \) A1
Note: If \(x = 360^\circ \) seen anywhere award A0
\(\tan x = \sqrt 3 \Rightarrow x = 60^\circ ,{\text{ }}240^\circ \) A1
\(\tan x = - \sqrt 3 \Rightarrow x = 120^\circ ,{\text{ }}300^\circ \) A1
[6 marks]
Examiners report
[N/A]
Syllabus sections
Topic 3 - Core: Circular functions and trigonometry » 3.6 » Algebraic and graphical methods of solving trigonometric equations in a finite interval, including the use of trigonometric identities and factorization.
Show 22 related questions
