If sin(x) = 2/3 and sec(y) = 5/4 , where x and y lie between 0 and π/2, evaluate sin(x + y).
Not sure if my answer is correct.
If sin(x)=2/3
Therefore,
X=sin^-1(2/3)
=41.81 degrees.(Approx.)
If sec(y)=5/4
Therefore, y=sec^-1(5/4)=36.84 degrees.(Approx.)
So we know now that
X=41.81 degrees
Y=36.841
Using addition formula for the sin.
here:
Sin(A+B)=Sin(A)*Cos(B)+Sin(B)*cos(A)
Let X=A , B=Y
Sin(41.81+36.841)=Sin(41.81)*Cos(36.841)+Sin(36.841)*Cos(41.81)=56.175 (degrees) =0.98 (Radians)
Let me know if I did any mistake.
If sin(x) = 2/3 and sec(y) = 5/4 , where x and y lie between 0 and π/2, evaluate sin(x + y).
Thanks guest,
It is really good to see you give the question a go.
Unfortunately, your answer cannot be fully correct because sine is a ratio. It is not going to be in degrees or radians.
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x and y are both acute angles.
Consider a right angled triangle with one acue angle equal to x
opp=2
hyp=3
so adj=sqrt(9-4) = sqrt 5
sinx=2/3 cosx=sqrt5 / 3
Consider a right angled triangle with one acue angle equal to x
cosy=4/5
adj=4
hyp=5
so opp=sqrt(16) = 4
sin(x+y)=sinxcosy+cosxsinysin(x+y)=23⋅45+√53⋅45sin(x+y)=20−4√515sin(x+y)=415(5−√5)
4/15(5-sqrt(5)) approx = 0.7370485393333894 This is a ratio, it is not going to be in degrees or radians.