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# sec(arctan(3/4))

How do you solve this?

### 3 Answers by Expert Tutors

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
1
Sec ( arc tan( 3/4) =

It is best to graph a right triangle

Mark one leg 3, and other  4 , then the hypotenuse  is

√ ( 3^2 + 4^2 ) = 5

Sec of the angle whose tangent is  3/4  = 1/ Cos ( arctan 3/4) = hypotenuse/ side adjacent

= 5/4

Sec ( arctan( 3/4) = 5/4

BRUCE S. | Learn & Master Physics & Math with Bruce SLearn & Master Physics & Math with Bruce...
4.9 4.9 (36 lesson ratings) (36)
1
arctan(3/4) means 'What angle has a tangent of 3/4 or 0.75'

The sec of that means 'What is the secant of that angle.

arctan(0.75) = 36.86 degrees

sec is the reciprocal of the cosine function

sec(36.86) = 1/cos(36.86) = 1/0.8 = 1.25

bds
Michael F. | Mathematics TutorMathematics Tutor
4.7 4.7 (7 lesson ratings) (7)
0
Evaluate sec(arc tan( 3/4) .  Let θ=arctan(3/4)
sec2θ=1+tan2θ=1+(3/4)2=1+9/16=25/16
secθ=5/4