How do I find the "exact value" for the arcsin of -pi/3 radians?
I hope you mean sine of -PI/3. ARCsin makes no sense, because you already have the angle.
PI radians is 180 deg, so PI/3 must be 60 deg. Now notice it is negative (300deg).
I assume you long ago memorized the 30-60-90 triangle functions.
That's weird, my paper clearly says arcsin of -pi/3 radians. So should I just say this isn't possible..or would -pi/3 still be the answer? or would i write -(sqrt 3)/2?
To find the exact value for the arcsin of -π/3 radians, you need to first understand what the arcsin function represents. The arcsin function, also known as the inverse sine function, gives the angle whose sine equals a given value.
In this case, you want to find the angle whose sine is -π/3. To do that, we can use a trigonometric identity. The identity states that sin(π/3) = sin(-π/3). This means that if we find the angle whose sine is π/3, it will have the same sine value as -π/3.
So, let's find the angle whose sine is π/3. We know that the sine of π/3 radians is equal to √3/2. Therefore, sin(π/3) = √3/2. Now, we can write the equation sin(θ) = √3/2, where θ represents the angle we are looking for.
To find the exact value, we take the inverse sine (or arcsin) of both sides of the equation. This cancels out the sine function on the left-hand side, and we are left with θ = arcsin(√3/2).
Using a calculator or a mathematical software, you can find that the value of arcsin(√3/2) is π/3.
Since we established that sin(π/3) = sin(-π/3), the exact value for arcsin(-π/3) is -π/3 radians.