Use the figure to find the exact value of the trigonometric function.
Sec 2θ
A = 1,b = 8

A) $\frac { 63 } { 64 }$
B) $\frac { 63 } { 65 }$
C) $\frac { 64 } { 65 }$
D) $\frac { 65 } { 63 }$
E) $\frac { 65 } { 64 }$

Question

Use the figure to find the exact value of the trigonometric function. ​
Sec 2θ​  ​
A = 1,b = 8
​
A)​ $\frac { 63 } { 64 }$ 
B) $\frac { 63 } { 65 }$ 
C)​ $\frac { 64 } { 65 }$ 
D)​ $\frac { 65 } { 63 }$ 
E) $\frac { 65 } { 64 }$

Quizplus · Accepted Answer

Using the Pythagorean identity, we have:

$A^2 + B^2 = C^2$

$1^2 + 8^2 = 65$

$\sqrt{65}$ is the hypotenuse.

Since we are dealing with $\sec 2	heta$, we want the adjacent side, which is $8$.

Therefore, $\sec 2	heta = \frac{	ext{hypotenuse}}{	ext{adjacent side}} = \frac{\sqrt{65}}{8}$

Rationalizing the denominator yields:

$\frac{\sqrt{65}}{8} \cdot \frac{\sqrt{65}}{\sqrt{65}} = \frac{65}{8\sqrt{65}} = \frac{65\sqrt{65}}{520} = \frac{\sqrt{65}}{8}$

Thus, the answer is D.

Use the Figure to Find the Exact Value of the Trigonometric