SOLUTION: Write the expression in terms of sine only. -√3sin(x) + cos(x) Write the expression in terms of sine only. 3(sin(2x) − cos(2x)) Write the given express

Algebra ->  Trigonometry-basics -> SOLUTION: Write the expression in terms of sine only. -√3sin(x) + cos(x) Write the expression in terms of sine only. 3(sin(2x) − cos(2x)) Write the given express      Log On


   

Question 1031176: Write the expression in terms of sine only.
-√3sin(x) + cos(x)


Write the expression in terms of sine only.
3(sin(2x) − cos(2x))

Write the given expression in terms of x and y only.
cos(sin^−1(x) − tan^−1(y))

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
Write the expression in terms of sine only.
-√3sin(x) + cos(x)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

-sqrt%283%29%2Asin%28x%29+%2B+cos%28x%29 = 2%2A%28%28-sqrt%283%29%2F2%29%2Asin%28x%29+%2B+%281%2F2%29%2Acos%28x%29%29 =         ( substitute here -sqrt%283%29%2F2 = cos(150°)  and  1%2F2 = sin(150°) )

= 2%2A%28cos%28150%5Eo%29%2Asin%28x%29+%2B+sin%28150%5Eo%29%2Acos%28x%29%29 =                   ( next use the formula  cos%28alpha%29%2Asin%28beta%29+%2B+sin%28alpha%29%2Acos%28beta%29 = sin%28alpha+%2B+beta%29 )

= 2sin(150° + x).

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