Question

Select one or more expressions that together represent all solutions to the equation. Your answer shouldbe in degrees. Assume n is any integer.8 sin(8x) + 9 = 3Choose all answers that apply:--48.59° + n. 180°-16.43° + n. 45--6.07° + n. 45-6.07° + n. 180

Answer 1

The solutions to the equation 8 sin(8x) + 9 = 3 are -48.59° + n(180°), where n is any integer.

To find the solutions to the equation 8 sin(8x) + 9 = 3, we can start by subtracting 9 from both sides to isolate the sine term: 8 sin(8x) = -6. Then, we divide both sides by 8 to get sin(8x) = -0.75.

To find the values of x, we need to find the inverse sine (sin^-1) of -0.75. Using a calculator, we find that sin^-1(-0.75) = -48.59°.

Since sin has a period of 360°, we can include the integer multiplier n to represent all possible solutions. The answers that apply to this equation are: -48.59° + n(180°), where n is any integer.

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