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# The point (-1,2) lies on the terminal side of theta in standard position. What are the exact values of sin theta, sec theta, and theta

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The point (-1,2) lies on the terminal side of theta in standard position. What are the exact values of sin theta, sec theta, and theta

Guest Feb 13, 2015

#1
+94101
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The point (-1,2) lies on the terminal side of theta in standard position. What are the exact values of sin theta, sec theta, and theta

theta is the obtuse angle with the vertex at (0,0)

$$\\sin\theta = \frac{opp}{hyp}=\frac{2}{\sqrt5}=\frac{2\sqrt5}{5}\\\\ Sec\theta=\frac{hyp}{adj}=\frac{\sqrt5}{-1}=-\sqrt5\\\\ \theta=180-atan(2)$$

$${\mathtt{180}}{\mathtt{\,-\,}}\underset{\,\,\,\,^{{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{2}}\right)} = {\mathtt{116.565\: \!051\: \!177\: \!078}}$$

$$\theta\approx 116.6\;\;degrees$$

Melody  Feb 13, 2015
#1
+94101
+10

The point (-1,2) lies on the terminal side of theta in standard position. What are the exact values of sin theta, sec theta, and theta

theta is the obtuse angle with the vertex at (0,0)

$$\\sin\theta = \frac{opp}{hyp}=\frac{2}{\sqrt5}=\frac{2\sqrt5}{5}\\\\ Sec\theta=\frac{hyp}{adj}=\frac{\sqrt5}{-1}=-\sqrt5\\\\ \theta=180-atan(2)$$

$${\mathtt{180}}{\mathtt{\,-\,}}\underset{\,\,\,\,^{{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{2}}\right)} = {\mathtt{116.565\: \!051\: \!177\: \!078}}$$

$$\theta\approx 116.6\;\;degrees$$

Melody  Feb 13, 2015