Y = 2sinx/(1+cosx+sinx)
Z=(1-cosx+sinx)/(1+sinx)
Options are:
1)z= 1-y
2)z= 1+y
3)z= 1/y
4)z=y
I just need a little push to understand what to do here
#Trigonometry
dull reef
onyx egretBOT
Y = 2sinx/(1+cosx+sinx)
Z=(1-cosx+sinx)/(1+sinx)
Options are:
1)z= 1-y
2)z= 1+y
...
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drifting sun
Y = 2sinx/(1+cosx+sinx)
Z=(1-cosx+sinx)/(1+sinx)
Options are:
1)z= 1-y
2)z= 1+y
...
Some brackets are needed. Otherwise, I'm not quite sure what you meant in each expression.
dull reef
Done
drifting sun
Y = 2sinx/(1+cosx+sinx)
Z=(1-cosx+sinx)/(1+sinx)
Options are:
1)z= 1-y
2)z= 1+y
...
Hm... Try multiplying the numerator and denominator of y by (1 - cos(x) + sin(x)).
drifting sun
That difference of squares in the denominator isn't quite correct. It should be (1 + sin(x))^2 - cos(x)^2.
Also, don't expand anything in the numerator yet. You'll see why a bit later.
drifting sun
Now what am I supposed to do?
Start by simplifying (1 + sin(x))^2 - cos(x)^2.
dull reef
Breaking 1+sinx^2 will give sin²x+ cos²x +2sinx -cos²x
Or do I use half angle formula to simplify 1+sinx?
drifting sun
Breaking 1+sinx^2 will give sin²x+ cos²x +2sinx -cos²x
Or do I use half angle fo...
Hm... That's not quite it. We have:
(1 + sin(x))^2 - cos(x)^2 = 1 + 2sin(x) + sin(x)^2 - cos(x)^2
Now, what is 1 - cos(x)^2?
drifting sun
Right, so that becomes 2sin(x)^2 + 2sin(x). And what can we do next?
dull reef
Do we separate the terms?
drifting sun
What do you mean?
drifting sun
Wait, no.
As I said, don't expand anything in the numerator. We have:
y = 2sin(x)/(1 + cos(x) + sin(x)) = 2sin(x)(1 - cos(x) + sin(x))/((1 + sin(x))^2 - cos(x)^2) = 2sin(x)(1 - cos(x) + sin(x))/(2sin(x)^2 + 2sin(x))
What can we do from here?
dull reef
Denominator 2sinx we take out?
drifting sun
Yeah, nice!
drifting sun
Nice, you're welcome!
dull reef
+close