Final answer:
To solve “sin(x°) = 5/7”, you must calculate the inverse sine of 5/7 using a calculator to find the primary angle solution. For all possible solutions, add integer multiples of 360° or consider symmetric angles in other quadrants.
Step-by-step explanation:
To solve for the variable when given sin(x°) = 5/7, you must determine the angle whose sine is 5/7. First, find the inverse sine (also known as arcsine) of 5/7 to determine the value of x in degrees. You would typically use a calculator for this, and it should be set to degree mode if it has the capability. The solution will be given by sin⁻¹(5/7).
However, it is important to note that sine is a periodic function and can have multiple solutions. The primary solution is the angle given directly by the inverse sine function. For all possible solutions, you would consider angles in other quadrants of the unit circle that share the same sine value. The general solutions would be of the form x = sin⁻¹(5/7) + 360°n or x = 180° - sin⁻¹(5/7) + 360°n, where n is an integer. In a school context, often only the principal value is required unless specified otherwise.