How to Find the Exact Values of Cosine and Sine of Compound Angles

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To find the exact values of cosine and sine for the angles x and y, given sin x = 3/5 and cos y = 5/13, one can use the Pythagorean identity sin²x + cos²x = 1 to derive cos x and sin y. For cos x, calculate √(1 - (3/5)²), resulting in cos x = 4/5. For sin y, calculate √(1 - (5/13)²), leading to sin y = 12/13. The discussion highlights the importance of using trigonometric identities to solve for unknown values in compound angles. Understanding these relationships is crucial for solving similar problems in trigonometry.
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Homework Statement



Angles x and y are located in the first quadrant such that sin x = 3/5 and cos y = 5/13.

a) Determine the exact value for cosx
b) Determine the exact value for siny


Homework Equations





The Attempt at a Solution



I don't know what to do.
Am I supposed to do something with the angle a+b?
 
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Use the expression sin2x + cos2x = 1, x being either alpha or beta :) .
 
oh jeez i feel dumb
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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