+0  
 
0
891
1
avatar

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

Best Answer 

 #1
avatar+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)

 

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

 

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

 

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

Melody  Feb 13, 2015
 #1
avatar+94101 
+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

36 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.