Assume sin A = sin B.
If A = π/8, find B.
Please show work so I'll know what to do.
if sin A = sin B
then clearly A = B
then if A = π/8
B = π/8
or B = π-A
To find the value of B when sin A = sin B, we can use the property of symmetric angles.
Given: sin A = sin B
Substituting A = π/8 into the equation: sin (π/8) = sin B
To solve this, we can use the inverse sine function (also known as arcsine) to find the angle B.
Step 1: Determine the principal value of sin (π/8)
Use a calculator to find the value of sin (π/8).
sin (π/8) ≈ 0.3827
Step 2: Solve for B
Now, using the inverse sine function, find the angle B by taking the arcsine of both sides of the equation.
arcsin (sin (π/8)) = arcsin (sin B)
Using a calculator: arcsin (0.3827) ≈ 0.3958
Therefore, B ≈ 0.3958 radians.
Note: Since sin function is periodic, there are infinitely many angles that satisfy sin A = sin B. However, by finding the principal value of sin A and taking the arcsine, we have found one possible value for B.