Question

What is the angle (in radians) corresponding to P(-0.34,-1.05)?

Answer 1

for clarification the point P is a point on the unit circle and lies in the third quadrant.

Answer 2

\(\large { \begin{array}{cccllll}
P(&-0.34,&-1.05)\\
&x&y\\
&adjacent&opposite
\end{array}
\\ \quad \\
tan(\theta)=\cfrac{opposite}{adjacent}\implies tan^{-1}[tan(\theta)]=tan^{-1}\left(\cfrac{opposite}{adjacent}\right)
\\ \quad \\
\theta=tan^{-1}\left(\cfrac{opposite}{adjacent}\right) }\)

Answer 3

I got you on this. You're right; it is in the third quadrant. x = -.34 and y = -1.05. The way we relate these sides is with the tangent identity. The tangent of A = -1.05/-.34. Divide that out and get 3.0823. Take the inverse tangent of that value to find the angle. It is 72 degrees, rounded to the nearest degree. To find it in radians, do this equivalency\[72\times \frac{ \pi }{ 180 }\]
and reduce between the 72 and the 180 to get \[\frac{ 4\pi }{ 5 }\]