Question

standard 18 homework
score: 4/22 answered: 4/17
question 5
evaluate the following expression. enter dne if the expression is undefined.
$sinleft(sin^{-1}(-0.2)
ight) = $
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Explanation:

Step1: Recall Inverse Sine Property

The sine function and its inverse, $\sin^{-1}(x)$ (also written as $\arcsin(x)$), are inverse functions. For a function $f(x)$ and its inverse $f^{-1}(x)$, the composition $f(f^{-1}(x)) = x$ holds for all $x$ in the domain of $f^{-1}(x)$. The domain of $\sin^{-1}(x)$ is $[-1, 1]$.

Step2: Check Domain and Apply Property

Here, the input to $\sin^{-1}$ is $-0.2$, and since $-1 \leq -0.2 \leq 1$, the expression $\sin^{-1}(-0.2)$ is defined. Then, using the property of inverse functions, $\sin(\sin^{-1}(-0.2))$ should equal the input of the inverse sine function, which is $-0.2$.

Answer:

$-0.2$