Questions: Write the trigonometric expression as an algebraic expression in u. sec(sin^(-1) u) sec(sin^(-1) u) = (Type an exact answer, using radicals as needed.)

Transcript text: Write the trigonometric expression as an algebraic expression in $u$. \[ \sec \left(\sin ^{-1} u\right) \] $\sec \left(\sin ^{-1} u\right)=$ $\square$ (Type an exact answer, using radicals as needed.)

Solution

Solution Steps

Step 1: Identify the Trigonometric Identity

Step 2: Express the Trigonometric Function in Terms of $u$

Given that $x = asin^-1(u)$, we express $\sec(x)$ in terms of $u$.

Step 3: Solve for the Desired Trigonometric Function

By algebraic manipulation, we find that $\sec(asin^-1(u)) = 1/sqrt(1 - u^2)$.

Step 4: Consider the Domain and Range

Ensure the solution is within the domain and range of the original and inverse trigonometric functions.

Final Answer: $\sec(asin^-1(u)) = (1 - u^2)^(-0.5)$

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Questions: Write the trigonometric expression as an algebraic expression in u. sec(sin^(-1) u) sec(sin^(-1) u) = (Type an exact answer, using radicals as needed.)

Solution

Solution Steps

Final Answer: \(\sec(asin^-1(u)) = (1 - u^2)^(-0.5)\)

Questions asked by other users