Question

Using a Calculator Use a calculator to evaluate the expression. Round your answer to five decimal places.

(a)$\mathit{c}\mathit{s}\mathit{c}\mathbf{}{\mathbf{10}}^{\mathbf{\circ }}$

(b)$\mathit{s}\mathit{i}\mathit{n}\mathbf{}{\mathbf{46}}^{\mathbf{\circ }}$

Short answer

(a).$\mathit{c}\mathit{s}\mathit{c}\mathbf{}{\mathbf{10}}^{\mathbf{\circ }}\mathbf{\approx }\mathbf{1}\mathbf{.83817}$

(b).role="math" localid="1648728942020" $\mathit{s}\mathit{i}\mathit{n}\mathbf{}{\mathbf{46}}^{\mathbf{°}}\mathbf{\approx }\mathbf{0}\mathbf{.901788348}$

Step-by-step solution

a. Step 1. Given information.

$\begin{array}{l}Given:\csc {10}^{\circ }\\ Tofind:Valueof\csc {10}^{\circ }uptofivedecimalplaces\\ Here,wewillusethecalculatortofindthevalue.\end{array}$

a. Step 2. Finding the value of csc10∘.

$\begin{array}{l}Wehave\csc {10}^{°}\\ Byusingcalculator,weget\\ \csc {10}^{°}\approx 1.83816396\\ \approx 1.83817\end{array}$

b. Step 1. Given information.

$\begin{array}{l}Given:\sin {46}^{\circ }\\ Tofind:Valueof\sin {46}^{\circ }uptofivedecimalplaces\\ Here,wewillusethecalculatortofindthevalue.\end{array}$

b. Step 2. Finding the value of sin46∘

$\begin{array}{l}Here,wewillusethecalculatortofindthevalue.\\ Wehave\sin {46}^{°}\\ Byusingcalculator,weget\\ \sin {46}^{°}\approx 0.901788348\\ \approx 0.90179\end{array}$