Find $\text { sect }$ given that $\sin t = - \frac { 3 } { 5 }$and $\tan t 0$

A) $\operatorname { sect } = \frac { 5 } { 3 }$

B) $\sec t = - \frac { 5 } { 3 }$

C) $\sec t = - \frac { 3 } { 4 }$

D) $\sec t = - \frac { 5 } { 4 }$

E) $\operatorname { sect } = \frac { 5 } { 4 }$

Question

Find $\text { sect }$ given that $\sin t = - \frac { 3 } { 5 }$and $\tan t > 0$

A) $\operatorname { sect } = \frac { 5 } { 3 }$

B) $\sec t = - \frac { 5 } { 3 }$

C) $\sec t = - \frac { 3 } { 4 }$

D) $\sec t = - \frac { 5 } { 4 }$

E) $\operatorname { sect } = \frac { 5 } { 4 }$

Quizplus · Accepted Answer

Since $	an t > 0$ and $\sin t = -\frac{3}{5}$, we know that $\cos t < 0$.

We can use the Pythagorean identity to solve for $\cos t$: 
$$\cos^2t + \sin^2t = 1$$
$$\cos^2t = 1 - \sin^2t = 1 - \left(-\frac{3}{5}ight)^2 = 1 - \frac{9}{25} = \frac{16}{25}$$
$$\cos t = -\frac{4}{5}$$

Now we can use the definition of $\sec$ to solve for $\sec t$: 
$$\sec t = \frac{1}{\cos t} = \frac{1}{-\frac{4}{5}} = -\frac{5}{4}$$

Therefore the answer is $\boxed{	extbf{(D)}\ \sec t = -\frac{5}{4}}$.

Find sect \text { sect } sect Given That sin⁡t=−35\sin t = - \frac { 3 } { 5 }sint=−53​

Find $\text { sect }$ Given That $\sin t = - \frac { 3 } { 5 }$