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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

 Feb 13, 2015

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 #1
avatar+118587 
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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)

 

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

 

$${\mathtt{180}}{\mathtt{\,-\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{2}}\right)} = {\mathtt{116.565\: \!051\: \!177\: \!078}}$$  

 

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

 Feb 13, 2015
 #1
avatar+118587 
+10
Best Answer

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)

 

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

 

$${\mathtt{180}}{\mathtt{\,-\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{2}}\right)} = {\mathtt{116.565\: \!051\: \!177\: \!078}}$$  

 

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

Melody Feb 13, 2015

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