How do you find the exact value of cos(arctan(3/4))

Aidyn Crosby

Aidyn Crosby

Answered question

2022-09-03

How do you find the exact value of cos ( arctan ( 3 4 ) )?

Answer & Explanation

Xavier Jennings

Xavier Jennings

Beginner2022-09-04Added 9 answers

Pose:
y = arctan ( 3 4 )
this means that:
tan y = 3 4
Using the trigonometric identity sec 2 t = 1 + tan 2 t :
1 cos 2 y = 1 + tan 2 y = 1 + 9 16 = 25 16
or:
cos 2 y = 16 25
and:
cos y = 4 5
where we take the positive root, since arctan ( 3 4 ) is in the interval ( 0 , π 2 )

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