find the two possible of x if 10sinx = 6 and 0 <=x<=180
You can divide 10 off of both sides... thus you need to know where sinx = .6 and if you sketch it you have a very accurate idea : )
To find the two possible values of x given that 10sin(x) = 6 and 0 <= x <= 180, we can follow these steps:
Step 1: Divide both sides of the equation by 10 to isolate the sine function:
sin(x) = 6/10
sin(x) = 0.6
Step 2: Take the inverse sin function (also known as arcsin or sin^(-1)) of both sides to find the value of x:
x = arcsin(0.6)
Now, using a calculator or the trigonometric table, we can find the value of arcsin(0.6), which is approximately 36.87 degrees.
So the first possible value of x is 36.87 degrees.
Step 3: Since 0 <= x <= 180, we know we need to find the second possible value of x in the range of 0 to 180 degrees.
To find the second possible value of x, we use the symmetry property of the sin function:
sin(x) = sin(180 - x)
Therefore, the second possible value of x is:
x = 180 - 36.87
x = 143.13 degrees.
So the two possible values of x are approximately 36.87 degrees and 143.13 degrees.
To find the two possible values of x in the given equation 10sinx = 6, we need to use inverse trigonometric functions, specifically the arcsine function.
Here's how you can do it step by step:
1. Start with the given equation: 10sin(x) = 6.
2. Divide both sides of the equation by 10 to isolate the sine term: sin(x) = 6/10 = 0.6.
3. Take the inverse sine (arcsine) of both sides of the equation to solve for x: x = arcsin(0.6).
4. Use a calculator or a trigonometric table to find the arcsine of 0.6. If using a calculator, make sure it is set to the correct angle unit (degrees or radians).
5. The arcsine of 0.6 can be determined to be approximately 36.87 degrees or 0.6435 radians.
At this point, we have found one possible value of x. However, we need to find the second possible value of x within the given range of 0 <= x <= 180.
6. To find the second possible value, subtract the first value from 180 degrees (or π radians) since the sine function is periodic.
180 degrees - 36.87 degrees = 143.13 degrees.
So, the two possible values of x that satisfy the equation 10sinx = 6 are approximately:
x = 36.87 degrees and x = 143.13 degrees.
Please note that these values are rounded to two decimal places and may be further approximations depending on the level of precision required.