Find the function values of cos θ, tan θ, sec θ, csc θ and cot θ ?

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Find the function values of cos θ, tan θ, sec θ, csc θ and cot θ ?

If sin θ = −(4)/(5)
and cos θ < 0, in which quadrant is θ? Find the function values of
cos θ, tan θ, sec θ, csc θ and cot θ.

1 Answer

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Answer 1 · 2018-02-13T19:16:42

Given that, $sin θ = (−4)/(5)$

applying the identity, $sin^2theta + cos^2 theta = 1$

$cos^2 theta = 1-sin^2theta$

$cos^2 theta = 1- ((-4)/5)^2$

$cos^2 theta = 1- 16/25 = 9/25$

$costheta = sqrt(9/25) = +-3/5$

its given that, $cos θ < 0$ ; $color(magenta)(costheta =(-3)/5$
Since, both $sintheta$ and $costheta$ are negative, $theta$ lies in the $color(red)("third quadrant")$ .

$tantheta = sintheta/costheta$
$=(-4)/5 xx 5/(-3) => color(magenta)(tantheta= 4/3$

$sec θ = 1/costheta => color(magenta)(sec theta=(-5)/3$

$csc θ = 1/sintheta => color(magenta)(csctheta = (-5)/4$

$cottheta = costheta/sintheta = 1/tantheta => color(magenta)(cottheta=3/4$

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Find the function values of cos θ, tan θ, sec θ, csc θ and cot θ ?

If sin θ = −(4)/(5)
and cos θ < 0, in which quadrant is θ? Find the function values of
cos θ, tan θ, sec θ, csc θ and cot θ.

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

Find the function values of cos θ, tan θ, sec θ, csc θ and cot θ ?

If sin θ = −(4)/(5) and cos θ < 0, in which quadrant is θ? Find the function values of cos θ, tan θ, sec θ, csc θ and cot θ.

1 Answer

Related questions

Impact of this question

If sin θ = −(4)/(5)
and cos θ < 0, in which quadrant is θ? Find the function values of
cos θ, tan θ, sec θ, csc θ and cot θ.