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sec(arctan(3/4))

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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 (6 lesson ratings) (6)
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