Question

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

(a).$\mathit{s}\mathit{i}\mathit{n}{\mathbf{22}}^{\mathbf{\circ }}$

(b).$\mathit{c}\mathit{o}\mathit{t}{\mathbf{23}}^{\mathbf{\circ }}$

Short answer

(a).$\mathit{s}\mathit{i}\mathit{n}{\mathbf{22}}^{\mathbf{°}}\mathbf{\approx }\mathbf{0}\mathbf{.37460}$

(b).$\mathit{c}\mathit{o}\mathit{t}{\mathbf{23}}^{\mathbf{°}}\mathbf{\approx }\mathbf{2}\mathbf{.35585}$

Step-by-step solution

a. Step 1. Given information.

$\begin{array}{l}\text{Given:}\sin {22}^{°}\\ \text{To\hspace{0.17em}\hspace{0.17em}find:Value\hspace{0.17em}\hspace{0.17em}of}\sin {22}^{°}\text{up\hspace{0.17em}to\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}five\hspace{0.17em}\hspace{0.17em}decimal\hspace{0.17em}\hspace{0.17em}places}\end{array}$

a. Step 2. Finding the value of sin22∘.

$\begin{array}{l}\text{Here,we\hspace{0.17em}\hspace{0.17em}will\hspace{0.17em}\hspace{0.17em}use\hspace{0.17em}\hspace{0.17em}the\hspace{0.17em}\hspace{0.17em}calculator\hspace{0.17em}\hspace{0.17em}to\hspace{0.17em}\hspace{0.17em}find\hspace{0.17em}\hspace{0.17em}the\hspace{0.17em}\hspace{0.17em}value.}\\ \text{We\hspace{0.17em}\hspace{0.17em}have}\sin {22}^{°}\text{By\hspace{0.17em}\hspace{0.17em}using\hspace{0.17em}\hspace{0.17em}calculator,}\\ \text{we\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}get}\sin {22}^{°}\approx 0.37460\end{array}$

b. Step 1. Given information

Given:$\cot {23}^{°}$

To find: Value of$\cot {23}^{°}$up to five decimal places

Here, we will use the calculator to find the value.

b. Step 2.Finding the value of cot23∘

$\begin{array}{l}\text{We\hspace{0.17em}\hspace{0.17em}have\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\cot {23}^{°}\\ \text{By\hspace{0.17em}\hspace{0.17em}using\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}calculator,weget}\\ \begin{array}{c}\cot {23}^{°}\approx 2.35585\\ \approx 2.35590\end{array}\end{array}$