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What is the exact values of 3 sinx= 0.90?

Answer 1

James Adkins

#x = sin^-1 0.3#

#3 sin x = 0.90# #sin x = 0.30#

#x = sin^-1 0.3#

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Answer 2

Abigail Armstrong

To find the exact values of (3 \sin(x) = 0.90), we first solve for (\sin(x)):

[3 \sin(x) = 0.90]

[\sin(x) = \frac{0.90}{3}]

[\sin(x) = 0.30]

The exact values of (x) for which (\sin(x) = 0.30) can be found using the inverse sine function, (\sin^{-1}):

[x = \sin^{-1}(0.30) + 2\pi n]

where (n) is an integer and (2\pi n) represents the periodic nature of the sine function.

So, the exact values of (x) satisfying (3 \sin(x) = 0.90) are:

[x = \sin^{-1}(0.30) + 2\pi n] [x = \sin^{-1}(0.30) + 2\pi n] [x \approx 0.304\pi + 2\pi n \text{ or } x \approx 2.838\pi + 2\pi n] [n \in \mathbb{Z}]

These values represent the solutions for (x) where (3 \sin(x) = 0.90), accounting for the periodicity of the sine function.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.