Question

If sin(x)=0.5 and cost(x) = -sqrt3/2, find x and tan
I get tan(x) and -1/sqrt3 is this correct? I then get arctan as being -30 but was told that is incorrect, any help please

Answer 1

sin is positive ,cos is negative
so angle lies in 2nd quadrant .

Answer 2

\[\sin x=0.5=\sin 30=\sin \left( 180-30 \right)=\sin 150\]
so x=150

Answer 3

tan x is correct.

Answer 4

why do you take 30 from 180? I am a bit confused

Answer 5

The problem is that tan(x) will give you same results for different 'x's.
For example, if your functions were \(sin(x) = -\frac{1}{2}\) and \(cos(x) = \frac{\sqrt{3}}{2}\) you would still get the same tan(x), but x will be different.

Let's do it the order they ask us to. Finding 'x' first.
We know that \(sin(x) = \frac{1}{2}\) means x is \(30^\circ\) or \((180^\circ - 30^\circ) = 150^\circ\)
But \(cos(30^\circ)\) is a positive value \(\frac{\sqrt{3}}{2}\) so x cannot be \(30^\circ\)
\(cos(150^\circ) = -\frac{\sqrt{3}}{2}\) which works. so we are left with \(x=150^\circ\) alone.
The tan as you calculated is correct, and is the same for \(tan(-30^\circ\)) and \(tan(150^\circ)\)

Answer 6

because angle in second quadrant.
and sin x=sin (180-x)

Answer 7

so how do I express the sin part as an answer

Answer 8

can I just say sin (x) = 180-30 = 150 therefore x = 150

Answer 9

no,sin x=sin(180-30)
or sin x=sin 150
x=150

Answer 10

ok thankyou :)