Use the fundamental identities to find the value of the trigonometric function.
-$\sec \theta$, if $\tan \theta = \frac { 3 } { 4 }$ and $\theta$ is in quadrant $\mathrm { I }$.
A) $- \frac { 3 } { 2 }$
B) $\frac { 5 } { 4 }$
C) $\frac { 3 \sqrt { 7 } } { 7 }$
D) $- \frac { \sqrt { 7 } } { 9 }$

Question

Quizplus · Accepted Answer

Given $\tan \theta = \frac{3}{4}$, we can use the Pythagorean identity to find $\sec \theta$. Since $\tan \theta = \frac{opposite}{adjacent}$, we have a right triangle where the opposite side is 3 and the adjacent side is 4. By the Pythagorean theorem, the hypotenuse is $\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$. Since $\sec \theta = \frac{1}{\cos \theta} = \frac{hypotenuse}{adjacent}$, $\sec \theta = \frac{5}{4}$.

Use the Fundamental Identities to Find the Value of the Trigonometric