The expression [tex]\sin(\cos^{-1}(-\frac{9}{\sqrt{145}}))[/tex] is a trigonometric expression, and the result of evaluating [tex]\sin(\cos^{-1}(-\frac{9}{\sqrt{145}}))[/tex] is [tex]\frac{8}{\sqrt{145}}[/tex]
How to evaluate the expression?
The expression is given as:
[tex]\sin(\cos^{-1}(-\frac{9}{\sqrt{145}}))[/tex]
In a right triangle, we have:
sin(x) = opp/hyp
cos(x) = adj/hyp
This means that:
hyp² = 145
adj = 9
The opposite side is then calculated using:
opp = √(hyp² - adj²)
So, we have:
opp = √(145 - 9²)
Evaluate
opp = √64
Evaluate
opp = 8
Recall that:
sin(x) = opp/hyp
So, we have:
[tex]\sin(x) = \frac{8}{\sqrt{145}}[/tex]
Hence, the result of evaluating [tex]\sin(\cos^{-1}(-\frac{9}{\sqrt{145}}))[/tex] is [tex]\frac{8}{\sqrt{145}}[/tex]
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