C2 sin question?

Solve the equation sin 2x = −0.5 for 0◦ < x < 180◦
So I thought this would be:
sin^-1 -0.5 gives us 2x then divide by 2?
But according to the answer it is 105 & 165?
Any help?

Reply 1

faizah007

sin^-1(-0.5)= -30
so 2x=-30
you can then use the quadrant method to find your two values by drawing the angle and reflecting it.
the two values will be
2x=180+30=210
so x=105....and
2x=360-30=330
so x=165

Reply 2

anonwinner

Are you familiar with trigonometric graphs? Trigonometric equations often have more than one root due to the nature of their graphs

Reply 3

Danny.L

Original post by anonwinner

Are you familiar with trigonometric graphs? Trigonometric equations often have more than one root due to the nature of their graphs

No, we havent come across trigs yet, just was hoping it was going to be simple. Apparently I was wrong.
Is it as tricky as it seems or does it just seem that way because this is the first time I've come across this type of thing?

Reply 4

anonwinner

Original post by Danny.L

Many questions will be more complicated than this, much more complicated in C3 and C4.

It may seem tricky now, but once you've practiced it for awhile it will seem easy.

I suggest you watch some of these videos (especially the last video about how to avoid losing solutions): http://examsolutions.net/maths-revision/core-maths/trigonometry/equations/squared-types/example-1.php

You should also watch these videos about how to use CAST diagrams: http://examsolutions.net/maths-revision/core-maths/trigonometry/quadrant-rule/tutorial-1.php

It isn't necessary to use CAST diagrams, but I find it much easier than using the trigonometric graphs