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# For what value of x does 6 sin (2x - 25)° attain its maximum value in the range...

### Question

For what value of x does 6 sin (2x - 25)° attain its maximum value in the range $$0^{\circ} \leq x \leq 180^{\circ}$$?

A) 12

B) 32

C) 57

D) 14

### Explanation:

$$y = 6\sin (2x - 25)$$;
$$\frac{\delta y}{\delta x} = 2 \cos (2x - 25)$$
Equating to zero gives:
$$12\cos (2x - 25) = 0$$
$$\cos(2x - 25) = 0$$
$$2x - 25 = \cos^{-1}0$$
$$2x - 25 = 90^{\circ};$$
$$2x = 90^{\circ} + 25^{\circ} = 115^{\circ}$$
$$2x = 115^{\circ};$$
$$x = \cfrac{115^{\circ}}{2}$$
$$x = 57\frac{1}{2}$$

## Dicussion (1)

• $$y = 6\sin (2x - 25)$$;
$$\frac{\delta y}{\delta x} = 2 \cos (2x - 25)$$
Equating to zero gives:
$$12\cos (2x - 25) = 0$$
$$\cos(2x - 25) = 0$$
$$2x - 25 = \cos^{-1}0$$
$$2x - 25 = 90^{\circ};$$
$$2x = 90^{\circ} + 25^{\circ} = 115^{\circ}$$
$$2x = 115^{\circ};$$
$$x = \cfrac{115^{\circ}}{2}$$
$$x = 57\frac{1}{2}$$