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Answer :
To determine the principal value of arcsin(0.98), we need to identify the angle in the range from [tex]\(-\frac{\pi}{2}\)[/tex] to [tex]\(\frac{\pi}{2}\)[/tex] where the sine is 0.98. This range is where the arcsin function is defined to give the principal value, which is the standard output of the inverse sine function.
The answer choices provided are in radians. Among the options:
- (A) -11.20
- (B) -4.91
- (C) 1.37
- (D) 7.65
We're looking for the angle that falls within the interval [tex]\(-\frac{\pi}{2}\)[/tex] to [tex]\(\frac{\pi}{2}\)[/tex] (approximately -1.57 to 1.57 in radians).
For [tex]\(\sin^{-1}(0.98)\)[/tex], the value we're looking for is the one closest to 1.37, which is indeed within the specified principal range. Therefore, the correct choice is:
(C) 1.37
This means that 1.37 radians is the principal value of [tex]\(\sin^{-1}(0.98)\)[/tex].
The answer choices provided are in radians. Among the options:
- (A) -11.20
- (B) -4.91
- (C) 1.37
- (D) 7.65
We're looking for the angle that falls within the interval [tex]\(-\frac{\pi}{2}\)[/tex] to [tex]\(\frac{\pi}{2}\)[/tex] (approximately -1.57 to 1.57 in radians).
For [tex]\(\sin^{-1}(0.98)\)[/tex], the value we're looking for is the one closest to 1.37, which is indeed within the specified principal range. Therefore, the correct choice is:
(C) 1.37
This means that 1.37 radians is the principal value of [tex]\(\sin^{-1}(0.98)\)[/tex].
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