find the two possible of x if 10sinx = 6 and 0 <=x<=180
sinx = 3/5
x = sin^-1(.6)
sin x = 6 / 10 = 3 / 5
First solution:
x = sin^-1 (0.6) = sin^-1 ( 3 / 5 )
x = 36.86989765°
Second solution:
Use identity:
sin ( 180° - x ) = sin x
sin ( 180° - 36.86989765° ) = 3 / 5
sin ( 143.13010235°) = 3 / 5
To find the two possible values of x, when 10sinx = 6 and 0 <= x <= 180, you can follow these steps:
Step 1: Divide both sides of the equation by 10 to isolate sin(x).
sin(x) = 6/10
sin(x) = 3/5
Step 2: Use the inverse sine function (sin^(-1)) to find the angle whose sine is 3/5.
x = sin^(-1)(3/5)
x ≈ 36.87 degrees
Step 3: Since the given range is 0 <= x <= 180, we need to find the other possible value.
The sine function is positive in both Quadrant I and Quadrant II. Since sin(x) = 3/5, and sin is positive in both those quadrants, the angle in Quadrant II with the same sine value can be obtained by subtracting the angle from 180 degrees.
x2 ≈ 180 - 36.87
x2 ≈ 143.13 degrees
Therefore, the two possible values of x are approximately 36.87 degrees and 143.13 degrees.
To find the two possible values of x if \(10 \sin(x) = 6\) and \(0 \leq x \leq 180\), we can follow these steps:
1. Rewrite the equation \(10 \sin(x) = 6\) as \(\sin(x) = \frac{6}{10}\) or \(\sin(x) = \frac{3}{5}\).
2. Since we are given \(0 \leq x \leq 180\), this means we are looking for values of \(x\) within the range of 0 to 180 degrees.
3. To find the two possible values of \(x\), we can use the inverse sine function, denoted as \(\sin^{-1}\) or \(\arcsin\), which gives us the angle with a specified sine value.
4. Use a calculator with an inverse sine function or consult a table of trigonometric values to find the angle whose sine is \(\frac{3}{5}\), which is approximately 36.87 degrees.
5. Since the sine function is periodic, it repeats every 360 degrees. Therefore, if \(\sin(x) = \frac{3}{5}\), the other possible solution will be \(180 - 36.87 = 143.13\) degrees.
6. Thus, the two possible values of \(x\) are approximately 36.87 degrees and 143.13 degrees.