Give the approximate answers as decimals, accurate to the nearest 0.001 . All tr

Question

Give the approximate answers as decimals, accurate to the nearest 0.001. All trigonometric functions are assumed to be in radians. Each problem is worth 2 points.

1. Rewrite the given function in the form acos(5x) + bsin(5x). Enter the missing coefficients as decimals accurate to within 0.001.
6cos(5x + 2.26) =   cos(5x) + sin(5x) 2. Rewrite the given function in the form acos(x) + bsin(x). Enter the missing coefficients as decimals accurate to within 0.001.
3sin(x 0.99) =   cos(x) + sin(x) 3. Rewrite the given function in the form Acos(7x ), where A > 0 and -/2 < < /2. Enter the missing coefficients as decimals accurate to within 0.001.
7cos(7x) 5sin(7x) =   cos(7x   ) 4. Let f(x) = cos(4x) + 7sin(4x).
Find the maximum value f(x) attains and the point x closest to 0 where it attains its max (since the function is periodic, it attains its max every 2/4 = /2). The maximum value of f(x) is = The value of x closest to 0 where this maximum is obtained is = 5.   Find all values of x with -pi<x<pi such that 8cos(x) + 2sin(x) = -5.52. Enter your answers as decimals rounded to the nearest 0.001, separating values with commas.
x =

Explanation / Answer

1)6cos(5x + 2.26)

cos(A+B)=cosAcosB-sinAsinB

=6cos(5x)cos(2.26) -6sin(5x)sin(2.26)

=6cos(2.26)cos(5x) -6sin(2.26)sin(5x)

=-3.186cos(5x)-4.631sin(5x)

===============================================

2)3sin(x 0.99)

sin(A-B)=sinAcosB-cosAsinB

=3(sin(x)cos(0.99)- cos(x)sin(0.99))

=3cos(0.99)sin(x)- 3sin(0.99)cos(x)

=1.646sin(x)-2.508cos(x)

=======================================

3)7cos(7x) 5sin(7x)

=(72+52)[(7/(72+52))cos(7x) (5/(72+52))sin(7x)]

=(74) [cos(7x) (7/74) sin(7x) (5/74)]

=8.602 [cos(7x+0.620)]

=8.602 [cos(7x+0.620-2)]

=8.602 cos(7x-5.633)

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