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

Question

Quizplus · Accepted Answer

In quadrant I, all trigonometric functions are positive. Given $\tan \theta = \frac{3}{4}$, we use the identity $\sec^2 \theta = 1 + \tan^2 \theta$. Calculating, $\sec^2 \theta = 1 + \left(\frac{3}{4}\right)^2 = 1 + \frac{9}{16} = \frac{25}{16}$. Thus, $\sec \theta = \sqrt{\frac{25}{16}} = \frac{5}{4}$.

Use the Fundamental Identities to Find the Value of the Trigonometric