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
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)
$$\\sin\theta = \frac{opp}{hyp}=\frac{2}{\sqrt5}=\frac{2\sqrt5}{5}\\\\
Sec\theta=\frac{hyp}{adj}=\frac{\sqrt5}{-1}=-\sqrt5\\\\
\theta=180-atan(2)$$
$${\mathtt{180}}{\mathtt{\,-\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{2}}\right)} = {\mathtt{116.565\: \!051\: \!177\: \!078}}$$
$$\theta\approx 116.6\;\;degrees$$
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)
$$\\sin\theta = \frac{opp}{hyp}=\frac{2}{\sqrt5}=\frac{2\sqrt5}{5}\\\\
Sec\theta=\frac{hyp}{adj}=\frac{\sqrt5}{-1}=-\sqrt5\\\\
\theta=180-atan(2)$$
$${\mathtt{180}}{\mathtt{\,-\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{2}}\right)} = {\mathtt{116.565\: \!051\: \!177\: \!078}}$$
$$\theta\approx 116.6\;\;degrees$$