Solve 11siny^2 = 13 - 3siny^2, where 0 < y <360. Round to the nearest tenth.?

Answer 1

11siny^2 = 13 - 3siny^2
14siny^2= 13
siny^2 =13/14
sin y = +/- sqrt(13/14)
sin y = +/- .9636
sin y = 74.5 degrees and 105.5 degrees.
sin y = -.9636
y = -74.49 degrees = 285. 5 degrees
y = 254.5 degrees

Answer 2

11siny^2=13-3siny^2 11siny^2+3siny^2=13
14siny^2=13 siny^2=13/14
y^2=360k+arcsin13/14 and y^2=360n+180-arcsin13/14
k=0 y^2=arcsin13/14 y=(arcsin13/14)^(1/2) the other response is negative and is not valid (0
k=1 y^2=360+arcsin13/14 after obtaining the root only the
positive response is valid.0
notice arcsin13/14=68.21 degree

... k=359 probably response exists.

for n also n=0 then n=1 ... n=359 probably.


you may use better expression for your question.ex. if the meaning of siny^2 be as (sin y)^(2) the answer will be very
simple as :
14((sin y)^(2))=13 then (sin y)^2=13/14 ,siny=(13/14)^(1/2)
the negative answer is not valid.

y=360k+arcsin((13/14)^(1/2)) and y=360n+180-arcsin((13/14)^(1/2))

where arcsin((13/14)^(1/2))=74.5 degree.

a big mistake from me
in all above answers the negative response is valid at some
multiples of 360 plus the arcsin ##.