jonnburton
Junior Member
- Joined
- Dec 16, 2012
- Messages
- 155
Hi,
I've been unable to fully solve an equation and can't see what step I am missing. Would anybody be able to tell me?
This is the question and my working:
Solve 4 sec 2x = -7 in the interval \(\displaystyle 0^{\circ} \leqslant x \leqslant 360^{\circ}\)
My working:
\(\displaystyle 4 \frac{1}{cos 2x} = -7\)
\(\displaystyle \frac{1}{cos 2x} = -\frac{7}{4}\)
\(\displaystyle cos 2x = \frac{1}{-\frac{7}{4}}\)
\(\displaystyle cos 2x = -\frac {4}{7}\)
\(\displaystyle 2x = 2.179 radians\)
\(\displaystyle 2x = 124.848^{\circ}\)
\(\displaystyle x = 62.4^{\circ}\) and \(\displaystyle x = 117.6^{\circ}\)
But the book gives two further answers: \(\displaystyle x = 242.4^{\circ}\) and \(\displaystyle x = 297.6^{\circ}\).
If anyone could tell me where the two further solutions come from I would be very grateful!
I've been unable to fully solve an equation and can't see what step I am missing. Would anybody be able to tell me?
This is the question and my working:
Solve 4 sec 2x = -7 in the interval \(\displaystyle 0^{\circ} \leqslant x \leqslant 360^{\circ}\)
My working:
\(\displaystyle 4 \frac{1}{cos 2x} = -7\)
\(\displaystyle \frac{1}{cos 2x} = -\frac{7}{4}\)
\(\displaystyle cos 2x = \frac{1}{-\frac{7}{4}}\)
\(\displaystyle cos 2x = -\frac {4}{7}\)
\(\displaystyle 2x = 2.179 radians\)
\(\displaystyle 2x = 124.848^{\circ}\)
\(\displaystyle x = 62.4^{\circ}\) and \(\displaystyle x = 117.6^{\circ}\)
But the book gives two further answers: \(\displaystyle x = 242.4^{\circ}\) and \(\displaystyle x = 297.6^{\circ}\).
If anyone could tell me where the two further solutions come from I would be very grateful!