1. Given that sin x =0.5 find the value of x between 90 and 360
you know that sin30 = 1/2
Use that as a reference angle
where else is sinx > 0 ?
sin x = 0.5. X = 30o N. of E. = 30o CCW.
sin x = 0.5. X = 30o N. of W. = 150o CCW.
solve it
To find the value of x between 90 and 360 degrees such that sin(x) = 0.5, you can use the inverse sine function (also known as arcsin or sin^(-1)). Here's how you can find the answer step by step:
Step 1: Convert the value of 0.5 to radians. Since the calculator functions work in radians, we need to convert the angle measure from degrees to radians. To do this, we multiply the value in degrees by π/180. Therefore, 0.5 radians is approximately 28.6479 degrees.
Step 2: Use the inverse sine function (arcsin) to find x. Using a calculator or mathematical software, apply the inverse sine function to 0.5. On most calculators, you can find the inverse sine function as "sin^(-1)" or "arcsin". When you enter arcsin(0.5), the calculator will give you the value of x, which is approximately 30 degrees (or 0.5236 radians).
Step 3: Check if the solution lies between 90 and 360 degrees. Since we are looking for a value of x between 90 and 360 degrees, we need to check if the solution we obtained in step 2 satisfies this condition. In this case, x = 30 degrees, which is indeed within the given range.
Therefore, the value of x between 90 and 360 degrees such that sin(x) = 0.5 is approximately 30 degrees.