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 $sinA$ :

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

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

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