How do you find the values of the other five trigonometric functions of the acute angle A with #tanA=3#?

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Answer 1 · 2018-03-19T15:34:16

See explanation.

First we can write that:

#cotA=1/tanA=1/3#

To find #sinA# and #cosA# we have to solve the system of equations:

#{ (sin^2A+cos^2A=1),(sinA/cosA=3):}#

To solve this equation we can calculate #sinA# from (2)

If we substitute to (1) we get:

#10cos^2A=1=>cos^2A=1/10 => cosA=sqrt(10)/10#

Now we can calculate #sinA#:

#sinA=3cosA=(3sqrt(10))/10#

#secA=1/cosA=sqrt(10)#

#cscA=1/sinA=10/(3sqrt(10))=sqrt(10)/3#