Question

Trigonometry question (Please help)

Answer 1

If 2sinx= 1, π/2 < x < π and √2 cos y =1 , 3 π/2 < y < 2 π , find the value of (tanx+tany )/(cosx-cosy)

Answer 2

I just need a hint i will show what i did

Answer 3

You can find x and y by taking the inverse sine and cosine respectively.
Just make sure that x and y are in the proper interval given.
Once x and y are known, the rest can be figured out.

Answer 4

We need a calc for inverse

Answer 5

These are standard angles in the unit circle.

Answer 6

Wait i will show what i did

Answer 7

\[\cos y =1/\sqrt{2}\]
\[\sin ^{2}y + \cos^{2}y =1 \]
\[\sin^{2}y=0.5 \]
\[\sin y = -\sqrt{0.5}\]
Following the same method \[Cos x = \sqrt{3}/2\]
\[\tan x = 1/\sqrt{3}\]

Answer 8

Is that correct ^

Answer 9

sin(y) = -sqrt(1/2) is correct.

But x is in the second quadrant where cos(x) is negative.

Answer 10

\[-\sqrt{3}/2\] ?

Answer 11

yes. so tan(x) will be negative too.

Answer 12

\[[-(1/\sqrt{3}) + (-1)]/-(\sqrt{3})/2- (1/\sqrt{2})]\]

Answer 13

Yes. You have to simplify them and it would take some work.

Answer 14

i simplified it