Greetings,
I have the problem below. I've tried dividing everything to sina or cosa - I get one or several tga's, but eventually I end up with a single sina or cosa with some other numbers and from there I loop...
Thank you.
If the trigonometric functions don't want to cooperate, bypass them and use the reference triangle of the angle instead.
tan(a) = -2
That means "a" is in the 2nd or 4th quadrants.
In the 2nd quadrant:
opposite side = 2
adjacent side = -1
hypotenuse = sqrt(5)
sin(a) = 2/sqrt(5)
cos(a) = -1/sqrt(5)
So,
sin(a) / [sin^3(a) +3cos^2(a)
= [2/sqrt(5)] / [(2/sqrt(5))^3 +3(-1/sqrt(5))^2]
= 0.67989 -------------answer.
In the 4th quadrant:
opposite side = -2
adjacent side = 1
hypotenuse = sqrt(5)
sin(a) = -2/sqrt(5)
cos(a) = 1/sqrt(5)
So,
sin(a) / [sin^3(a) +3cos^2(a)
= [-2/sqrt(5)] / [(-2/sqrt(5))^3 +3(1/sqrt(5))^2]
= 7.74116 -------------answer also.