We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
96
4
avatar

If sin(x) = 2/3 and sec(y) = 5/4 , where x and y lie between 0 and π/2, evaluate sin(x + y).

 Sep 1, 2019
edited by Guest  Sep 1, 2019
 #1
avatar
+1

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. 

 Sep 1, 2019
 #2
avatar+105634 
+2

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.

----------------

 

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

 

\(sin(x+y)=sinx cosy+cosxsiny\\ sin(x+y)=\frac{2}{3} \cdot\frac{4}{5}+\frac{\sqrt5}{3}\cdot\frac{4}{5}\\ sin(x+y)=\frac{20-4\sqrt5}{15}\\ sin(x+y)=\frac{4}{15}(5-\sqrt5)\)

 

4/15(5-sqrt(5)) approx = 0.7370485393333894    This is a ratio, it is not going to be in degrees or radians.

 Sep 1, 2019
 #3
avatar+104836 
+2

sin (x)  = 2/3      ⇒  cos(x)   =  √[3^2 - 2^2]  / 3  =  √[5]/3

sec (y)  =  5/4  ⇒  cos (y)   =  4/5  ⇒  sin(y)   =  3/5

 

sin (x + y)   =  sin (x) cos (y)  + cos (x)  sin( y )  =

 

(2/3)(4/5)  + (√5)/3 (3/5)  =

 

[ 8   + 3√5 ]                       

_________               

     15                

 

 

cool cool cool               

 Sep 1, 2019
 #4
avatar+105634 
0

Since Chris has answered after me I assume I made a silly mistake somewhere.

 Sep 2, 2019

11 Online Users

avatar