sec(arctan(3/4))

Question

How do you solve this?

Answer 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

 

Answer 2

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

Answer 3

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