Question

Nossis has been working on his geometry homework and he is almost finished. His last task is to find a solution of sin x=0.75. Nossis cannot figure out what x could be! Explain how he can find a value for x and show that it works.

Answer 1

Nossis can find the value of x for sin x=0.75 using the inverse sine function on a scientific calculator. He will get one value in the first quadrant and should remember to also calculate the equivalent angle in the second quadrant where sine is also positive. Finally, he should verify the solution by calculating the sine of the resulting angles.

Step-by-step explanation:

To find a solution for sin x=0.75, Nossis can use a scientific calculator to find the angle whose sine is 0.75. This can be done by inputting the inverse sine function, which is typically labeled as 'sin⁻¹' or 'arcsin' on calculators. By entering 'arcsin(0.75)' into the calculator, Nossis will get a principal value for x in the first quadrant since sin x is positive.

However, because the sine function is positive in both the first and second quadrants, Nossis should also find the value in the second quadrant which can be computed as 180 degrees minus the principal value. If Nossis needs the answer in radians, he can convert degrees to radians by multiplying the angle in degrees by π/180.

To verify the solution works, Nossis would calculate sin(x) of the resultant angles and check if it equals 0.75. It is important to note that the sine function is periodic with a period of 2π, so there are infinitely many solutions, but typically one solution in degrees or radians is sought in schoolwork unless the question specifies an interval for x.