Question

10 sin² x + 9 sin x - 7=0​

Answer 1

Ответ:

10 * sin^2 x+9 sin x - 7=0

10* six^2 x+9 six - 7=0

10 * 6^2 x+9 6-7=0

10*36 x+9* - 1=0

Answer 2

To solve the quadratic equation 10sin²(x) + 9sin(x) - 7 = 0 for sin(x), you can use the quadratic formula:

sin(x) = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 10, b = 9, and c = -7. Plug these values into the formula:

sin(x) = (-9 ± √(9² - 4 * 10 * (-7))) / (2 * 10)

sin(x) = (-9 ± √(81 + 280)) / 20

sin(x) = (-9 ± √361) / 20

Now, calculate the two possible values for sin(x):

1. sin(x) = (-9 + √361) / 20 sin(x) = (7/20)

2. sin(x) = (-9 - √361) / 20 sin(x) = (-16/20) sin(x) = (-4/5)

So, the solutions for sin(x) are sin(x) = 7/20 and sin(x) = -4/5.

To find the values of x, you can use the inverse sine function (arcsin):

1. For sin(x) = 7/20: x₁ = arcsin(7/20) (in radians) x₁ ≈ 0.343 radians (approximately)

2. For sin(x) = -4/5: x₂ = arcsin(-4/5) (in radians) x₂ ≈ -0.927 radians (approximately)

Remember that there are infinitely many solutions to trigonometric equations, so these are just a couple of possible solutions within a certain range. Depending on your context, you might need to consider additional solutions in other intervals.