Question

Given that tan^2 e= 3/8 what is the value of sec e? A. +√8/3 B.+ √11/8 C. 11/8 D. 8/3

Answer 1

ANSWER

${ \sec}(e) = \pm \: \sqrt{\frac{11}{8} }$

EXPLANATION

We use the Pythagorean Identity,

${ \sec}^{2} (e) = 1 + { \tan}^{2} (e)$

It was given that,

${ \tan}^{2} (e) = \frac{3}{8}$

We substitute the values into the identity to obtain,

${ \sec}^{2} (e) = 1 + \frac{3}{8}$

${ \sec}^{2} (e) = \frac{11}{8}$

We take square root of both sides to get,

${ \sec}(e) = \pm \: \sqrt{\frac{11}{8} }$

Answer 2

Answer:

sec e = √(11/8) ⇒ answer B

Step-by-step explanation:

* Lets revise some identities in trigonometry

# sin²x + cos²x = 1

- Divide both sides by cos²x

∴ sin²x/cos²x + cos²x/cos²x = 1/cos²x

∵ sinx/cosx = tanx

∴ sin²x/cos²x = tan²x

∵ cos²x/cos²x = 1

∵ 1/cosx = secx

∴ 1/cos²x = sec²x

* Now lets write the new identity

# tan²x + 1 = sec²x

- Let x = e

∴ tan²e + 1 = sec²e

- Substitute the value of tan²e in the identity

∵ tan²e = 3/8

∴ 3/8 + 1 = sec²e

- Change the 1 to the fraction 8/8

∴ 3/8 + 8/8 = sec²e ⇒ add the fractions

∴ 11/8 = sec²e

- Take square root for the two sides to find sec e

∴ sec e = √(11/8)

∴ The answer is B