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Tutorial Exercise

Find the exact value of the expression, if possible.

[tex]\[ \cos \left(\arcsin \left(\frac{8}{17}\right)\right) \][/tex]

Step 1

Recall the definition of the inverse trigonometric functions.

The inverse sine function is defined by [tex]\( y = \arcsin(x) \)[/tex] if and only if [tex]\( \sin(y) = x \)[/tex], with appropriate restrictions on the domain.

Let [tex]\( u = \arcsin \left(\frac{8}{17}\right) \)[/tex].

According to the definition, what is the value of [tex]\( \sin(u) \)[/tex]?

[tex]\[ \sin(u) = \][/tex]

[tex]\[ \boxed{\frac{8}{17}} \][/tex]



Answer :

GinnyAnswer
To find the value of [tex]\(\sin(u)\)[/tex] where [tex]\(u = \arcsin\left(\frac{8}{17}\right)\)[/tex], we use the definition of the inverse sine function.

The inverse sine function, [tex]\(\arcsin(x)\)[/tex], returns an angle [tex]\(u\)[/tex] such that [tex]\(\sin(u) = x\)[/tex]. Given:
[tex]\[ u = \arcsin\left(\frac{8}{17}\right) \][/tex]

Therefore,
[tex]\[ \sin(u) = \frac{8}{17} \][/tex]

So the value of [tex]\(\sin(u)\)[/tex] is:
[tex]\[ \sin(u) = \frac{8}{17} \][/tex]