If the terminal point determined by $t$ is $\left( \frac { 12 } { 13 } , - \frac { 5 } { 13 } \right)$, find $\sin t$, $\cos t$And $\tan t$

A) $\sin ( t ) = \frac { 12 } { 13 }$, $\cos ( t ) = \frac { 5 } { 13 }$, $\tan ( t ) = \frac { 5 } { 12 }$

B) $\sin ( t ) = - \frac { 5 } { 13 }$, $\cos ( t ) = \frac { 12 } { 13 }$, $\tan ( t ) = - \frac { 5 } { 12 }$

C) $\sin ( t ) = \frac { 5 } { 13 }$, $\cos ( t ) = - \frac { 12 } { \Gamma 3 }$, $\tan ( t ) = - \frac { 13 } { 12 }$

D) $\sin ( t ) = - \frac { 5 } { 13 }$, $\cos ( t ) = \frac { 12 } { 13 }$, $\tan ( t ) = - \frac { 12 } { 5 }$

E) $\sin ( t ) = - \frac { 5 } { 13 }$, $\cos ( t ) = \frac { 12 } { 13 }$, $\tan t = \frac { 12 } { 5 }$

Question

If the terminal point determined by $t$ is $\left( \frac { 12 } { 13 } , - \frac { 5 } { 13 } \right)$, find $\sin t$, $\cos t$And $\tan t$

A) $\sin ( t ) = \frac { 12 } { 13 }$, $\cos ( t ) = \frac { 5 } { 13 }$, $\tan ( t ) = \frac { 5 } { 12 }$

B) $\sin ( t ) = - \frac { 5 } { 13 }$, $\cos ( t ) = \frac { 12 } { 13 }$, $\tan ( t ) = - \frac { 5 } { 12 }$

C) $\sin ( t ) = \frac { 5 } { 13 }$, $\cos ( t ) = - \frac { 12 } { \Gamma 3 }$, $\tan ( t ) = - \frac { 13 } { 12 }$

D) $\sin ( t ) = - \frac { 5 } { 13 }$, $\cos ( t ) = \frac { 12 } { 13 }$, $\tan ( t ) = - \frac { 12 } { 5 }$

E) $\sin ( t ) = - \frac { 5 } { 13 }$, $\cos ( t ) = \frac { 12 } { 13 }$, $\tan t = \frac { 12 } { 5 }$

Quizplus · Accepted Answer

In a unit circle, the x-coordinate represents $\cos(t)$ and the y-coordinate represents $\sin(t)$. Therefore, $\cos(t) = \frac{12}{13}$ and $\sin(t) = -\frac{5}{13}$. The tangent function is the ratio of sine over cosine, so $\tan(t) = \frac{\sin(t)}{\cos(t)} = \frac{-\frac{5}{13}}{\frac{12}{13}} = -\frac{5}{12}$.

If the Terminal Point Determined By ttt Is (1213,−513)\left( \frac { 12 } { 13 } , - \frac { 5 } { 13 } \right)(1312​,−135​)

If the Terminal Point Determined By $t$ Is $\left( \frac { 12 } { 13 } , - \frac { 5 } { 13 } \right)$