What is the exact value of sin^-1(sin(8pi/15)?
You have to be kidding. 8PI/15
what is the exact angle of arccosine (cosine PI)? Answer: PI
To find the exact value of sin^-1(sin(8π/15)), you can follow these steps:
Step 1: Determine the principal value
The principal value of an inverse trigonometric function is the value that lies within the range of the function. For the sine function, the range is [-π/2, π/2].
Step 2: Find the equivalent angle
Since sin(x) repeats itself after every 2π, we can find an equivalent angle within the range of [-π/2, π/2] by subtracting or adding multiples of 2π. In this case, we can rewrite 8π/15 as an equivalent angle within the principal range.
8π/15 = 2π/15
Step 3: Evaluate the inverse sine function
The inverse sine function, sin^(-1)(x) or arcsin(x), gives the angle whose sine is x. In this case, we are looking for the angle whose sine is sin(2π/15).
So, sin^(-1)(sin(8π/15)) = sin^(-1)(sin(2π/15))
Now, since sin and sin^(-1) are inverses of each other, the two functions cancel each other out, and we are left with:
sin(8π/15) = sin(2π/15)
Therefore, the exact value of sin^-1 (sin(8π/15)) is sin(2π/15).