Respuesta :
Answer:
621 /629
Step-by-step explanation:
The formula for sin (x+y) is sin x cosy + cos x sin y.
opposite side
If sin y 12/37 (which is equal to ----------------------- ) we can find the length
hypotenuse
of the adjacent side as follows. Representing the adjacent side by x, we get
37^2 = x^2 + 12^2 (following the Pythagorean Theorem).
Then 1369 = x^2 + 144, or x^2 = 1225, so that x must be +√1225, or +35.
Thus, the cosine of y is (adj side) / (hypo) = 35/37.
√(17^2 - 8^2) √225
Similarly, the sine of angle x is -------------------- = ----------- = 15/17
17 17
In summary, sin x = 15/17; cos x = 8/17; sin y = 12/37 and cos y =35/37.
We now substitute these values into the formula
sin (x+y) is sin x cosy + cos x sin y:
sin (x+y) = (15/17)(35/37) + (8/17)(12/37)
525 96 621
= --------------- + -------------- = ------------ = 621 /629
629 629 629
The exact value is 621/629.
How to calculate the exact value of sin(x+y)?
sin (x+y) = sin x cos y+sin y cos x
If cos x = 8/17 and sin y = 12/32
and [tex]$\cos ^{2} y+\sin ^{2} y=1$[/tex]
To calculate sin x and cos y
[tex]$\sin ^{2} x=1-\cos ^{2} x=1-\left(\frac{8}{17}\right)^{2}=\frac{225}{17^{2}}$[/tex]
[tex]$\sin x=\frac{15}{17}$[/tex]
[tex]$\cos ^{2} y=1-\sin ^{2} y=1-\left(\frac{12}{37}\right)^{2}=\frac{1225}{37^{2}}$[/tex]
[tex]$\cos y=\frac{35}{37}$[/tex]
so,
[tex]$\sin (x+y)=\frac{15}{17} \cdot \frac{35}{37}+\frac{12}{37} \cdot \frac{8}{17}=\frac{621}{629}$[/tex]
Therefore the exact value is 621/629.
To learn more about the exact value, refer:
https://brainly.com/question/1603720
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