Question

find period f(x)=3 sin√5x +4cos√50x​

Answer 1

you can got it answer by this method

Use the form asin(bx−c)+dasin(bx-c)+d to find the variables used to find the amplitude, period, phase shift, and vertical shift.

a=3a=3

b=1b=1

c=0c=0

d=4cos(5√2x)d=4cos(52x)

Find the amplitude |a||a|


Find the amplitude |a||a|.

Amplitude: 33

Find the period using the formula 2π|b|2π|b|.

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The period of the function can be calculated using 2π|b|2π|b|.

Period: 2π|b|2π|b|

Replace bb with 11 in the formula for period.

Period: 2π|1|2π|1|

Solve the equation.

The absolute value is the distancebetween a number and zero. The distance between 00 and 11 is 11.

Period: 2π12π1

Divide 2π2π by 11.

Period: 2π2π

Find the phase shift using the formula cbcb.

The phase shift of the function can be calculated from cbcb.

Phase Shift: cbcb

Replace the values of cc and bb in the equation for phase shift.

Phase Shift: 0101

Divide 00 by 11.

Phase Shift: 00

Find the vertical shift dd.

Vertical Shift: 4cos(5√2x)4cos(52x)

List the properties of the trigonometric function.

Amplitude: 33

Period: 2π2π

Phase Shift: 00 (00 to the right

Vertical Shift: 4cos(5√2x)