evaluate sin^-1(negative square route of 3over2) in radians.
To evaluate sin^-1 of a value in radians, you can use the trigonometric identity:
sin(sin^-1(x)) = x
Let's solve the equation step by step:
Given: sin^-1(-√3/2)
Step 1: Sin^-1(-√3/2) = α (Let's assume this value as α)
Step 2: Apply the sin function to both sides of the equation:
sin(α) = -√3/2
Step 3: Now, think about the trigonometric unit circle and recall the values of sin for the common angles:
sin(30 degrees) = 1/2
sin(45 degrees) = √2/2
sin(60 degrees) = √3/2
In this case, we can see that -√3/2 matches the value of sin(240 degrees).
Step 4: Convert 240 degrees to radians by multiplying it by π/180:
240 degrees * (π/180) = 4π/3 radians
Therefore, sin^-1(-√3/2) in radians is equal to 4π/3.
Remember, when evaluating inverse trigonometric functions, always keep in mind the ranges and principal values for each function.