Find the exact value of Sin^-1(sin(13pi/15))
ummmhhh, wouldn't that just be 13π/15 ?
or, since the sine is + in both the 2nd or 1st quadrant, and
since 13π/15 is in quadrant II we could also have
π - 13π/15 = 2π/15
check with calculator, set to radians
enter:
13
x
π
÷
15
=
sin
=
2nd sin
= .41887902 which is 2π/15
To find the exact value of sin^(-1)(sin(13π/15)), we need to understand the concept of inverse trigonometric functions and how they work.
In mathematics, the inverse trigonometric functions (sin^(-1), cos^(-1), tan^(-1), etc.) provide a way to "undo" the trigonometric functions (sin, cos, tan) and retrieve the original angle.
In this case, we have sin^(-1)(sin(13π/15)). The outer function, sin^(-1), is the inverse sine or arcsine function, and the inner function is sin(13π/15).
To find the value of this expression, follow these steps:
Step 1: Rewrite the angle within the range [-π/2, π/2).
- The arcsine function returns an angle within that range.
- The original angle is 13π/15, which is not within this range.
- To bring it within the range, subtract or add multiples of 2π until you get an equivalent angle within the range.
- 13π/15 is already relatively close to π/2, so we subtract 2π to bring it closer.
- Let's subtract 2π from 13π/15: 13π/15 - 2π = -17π/15
Step 2: Evaluate the arcsine function with the new angle.
- Since -17π/15 is now in the range [-π/2, π/2), we can find its arcsine value.
- arcsin(-17π/15) = -0.6807 radians (approximately)
So, the exact value of sin^(-1)(sin(13π/15)) is -0.6807 radians (approximately).