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

Question

Give the approximate answers as decimals, accurate to the nearest 0.001. All trigonometric functions are assumed to be in radians.

1)Rewrite the given function in the form acos(2x) + bsin(2x). Enter the missing coefficients as decimals accurate to within 0.001.
3cos(2x - 0.38) = ________cos(2x) + ________sin(2x)

2)Rewrite the given function in the form acos(3x) + bsin(3x). Enter the missing coefficients as decimals accurate to within 0.001.
6sin(3x - 1.81) =________cos(3x) +________ sin(3x)

4)Let f(x) = 5cos(5x) + sin(5x).
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 2pi/5).
    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=______________________________________________

Give the approximate answers as decimals, accurate to the nearest 0.001. All trigonometric functions are assumed to be in radians. 1)Rewrite the given function in the form acos(2x) + bsin(2x). Enter the missing coefficients as decimals accurate to within 0.001. 3cos(2x - 0.38) = ________cos(2x) + ________sin(2x) 2)Rewrite the given function in the form acos(3x) + bsin(3x). Enter the missing coefficients as decimals accurate to within 0.001. 6sin(3x - 1.81) =________cos(3x) +________ sin(3x) 3)Rewrite the given function in the form Acos(5x - phi 0 and -pi/2

Explanation / Answer

1) 3cos(2x - 0.38) = cos(2x) cos(0.38) + sin(2x) sin(0.38) = 2.878 cos(2x) + 1.113 sin(2x) (ans)

2) 6sin(3x + 1.81) =sin(3x) cos(1.81) + cos(3x) sin(1.81) = 5.829 cos(3x) -1.422 sin(3x) (ans)

3) 4cos(5x) - 6sin(5x) = sqrt(4^2+6^2) cos(5x - arctan(6/4) ) = 7.211 cos( 5x - 0.982) (ans)

4) f(x) = 5cos(5x) + sin(5x) = sqrt ( 5^2 + 1^2) sin (5x + arctan(5) ) = 5.099 sin ( 5x + 1.373)

So maximum value of f(x) = 5.099 (ans)

The value of x closest to 0 where this maximum is obtained is when

5x + 1.373 = 0 , 3.14

x= -0.2746 , 0.3534

The value of x closest to 0 where this maximum is obtained is x = -0.2746 radians (ans)

5) 6cos(2x) + 5sin(2x) = -1.72

sqrt(5^2 +6^2) sin ( 2x + arctan(6/5) = 7.810 sin ( 2x + 0.876) = -1.72

2x + 0.876 = -.0.222 , 3.362 , -2.918 , 6.058

x= -0.549 , 1.243 , -1.897 , 2.591 (ans)

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