Find the exact value of each of the six trigonometric functions of $θ$ , if $(4, 1)$ is a point on the terminal side of angle $θ$ .
$\sin θ =$
(Simplify your antwer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

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Answer

$\sin θ = \frac{\sqrt{17}}{17}, \cos θ = \frac{4 \sqrt{17}}{17}, \tan θ = \frac{1}{4}, \csc θ = \sqrt{17}, \sec θ = \frac{\sqrt{17}}{4}, \cot θ = 4$

Steps

Step 1 ： $r = \sqrt{(x^{2}) + (y^{2})} = \sqrt{(4^{2}) + (1^{2})} = \sqrt{16 + 1} = \sqrt{17}$

Step 2 ： $\sin θ = \frac{y}{r} = \frac{1}{\sqrt{17}} = \frac{\sqrt{17}}{17}$

Step 3 ： $\cos θ = \frac{x}{r} = \frac{4}{\sqrt{17}} = \frac{4 \sqrt{17}}{17}$

Step 4 ： $\tan θ = \frac{y}{x} = \frac{1}{4}$

Step 5 ： $\csc θ = \frac{r}{y} = \frac{\sqrt{17}}{1} = \sqrt{17}$

Step 6 ： $\sec θ = \frac{r}{x} = \frac{\sqrt{17}}{4}$

Step 7 ： $\cot θ = \frac{x}{y} = \frac{4}{1} = 4$

Step 8 ： $\sin θ = \frac{\sqrt{17}}{17}, \cos θ = \frac{4 \sqrt{17}}{17}, \tan θ = \frac{1}{4}, \csc θ = \sqrt{17}, \sec θ = \frac{\sqrt{17}}{4}, \cot θ = 4$

Find the exact value of each of the six trigonometric functions of θ, if (4,1) is a point on the terminal side of angle θ.sin⁡θ=(Simplify your antwer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

Answer

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Find the exact value of each of the six trigonometric functions of $θ$ , if $(4, 1)$ is a point on the terminal side of angle $θ$ .
$\sin θ =$
(Simplify your antwer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)