Solve sin(x) = -0.36 on 0 le x lt 2pi
There are two solutions, A and B, with A < B and A and B in radians to 4 decimal places.
le= (less than or equal to)
lt= (less than)
Here is how I do these.
First I decide in which quadrant the angles are.
Since sinx is negative, x must be in quads III or IV.
I then find the angle in standard position by finding sin^-1 (+.36) which is
.36826.. (in radians) or 21.1 degrees
so x = pi + .36826 or x = 2pi - .36826
in degrees x = 201.1 or 338.9
Thank you for your help!
To solve the equation sin(x) = -0.36 on the interval 0 ≤ x < 2π, we can use the inverse sine function, also known as arcsin. However, it's important to note that the arcsin function returns just one value, but we are looking for two solutions.
To find the first solution, let's use the arcsin function:
x₁ = arcsin(-0.36)
To evaluate this, you can use a scientific calculator or an online calculator by inputting the value -0.36 and taking the arcsin. Make sure your calculator is set to radians mode.
Once you have the value of x₁, you will find that it gives you an angle in radians between -π/2 and π/2. However, since we are looking for solutions in the range 0 ≤ x < 2π, we need to add 2π to the result if necessary:
x₁ = x₁ + 2π
Now, let's find the second solution. We can use the fact that sin(x) has a periodicity of 2π. Therefore, we can write the equation as:
sin(x) = -0.36 = sin(x + 2π)
To find the second solution, we can solve the equation:
x₂ + 2π = arcsin(-0.36)
Then:
x₂ = arcsin(-0.36) - 2π
Again, evaluate this using a calculator in radians mode. If the result is negative, we need to add 2π to obtain a solution in the desired range.
x₂ = x₂ + 2π (if x₂ < 0)
Finally, you should have two solutions, A and B, with A < B. Round these solutions to four decimal places, as requested.