How do you find the values of the six trigonometric functions given $tan θ = - \frac{15}{8}$ $tantheta=-15/8$ and $sin θ < 0$ $sintheta<0$ ?

Question

How do you find the values of the six trigonometric functions given $tan θ = - \frac{15}{8}$ $tantheta=-15/8$ and $sin θ < 0$ $sintheta<0$ ?

1 Answer

Impact of this question

13586 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-15T06:40:23

$sin θ = - \frac{15}{17}$ $sintheta=-15/17$ , $cos θ = \frac{8}{17}$ $costheta=8/17$ , $tan θ = - \frac{15}{8}$ $tantheta=-15/8$
$cot θ = - \frac{8}{15}$ $cottheta=-8/15$ , $sec θ = \frac{17}{8}$ $sectheta=17/8$ , $csc θ = - \frac{17}{15}$ $csctheta=-17/15$

Explanation:

As $tan θ = - \frac{15}{8}$ $tantheta=-15/8$ and $sin θ < 0$ $sintheta<0$ i.e. both are negative,

$θ$ $theta$ is in Q4 - fourth quadrant and while $cos θ$ $costheta$ and $sec θ$ $sectheta$ are positive, rest of the four trigonometric functions are negative.

Now as $tan θ = - \frac{15}{8}$ $tantheta=-15/8$ , $cot θ = - \frac{8}{15}$ $cottheta=-8/15$ and

$sec θ = \sqrt{1 + {tan}^{2} θ} = \sqrt{1 + \frac{225}{64}} = \frac{\sqrt{289}}{64} = \frac{17}{8}$ $sectheta=sqrt(1+tan^2theta)=sqrt(1+225/64)=sqrt289/64=17/8$

$:.costheta=1/sectheta=8/17$

$sintheta=tanthetaxxcostheta=-15/8xx8/17=-15/17$

and $csctheta=-17/15$

Science

Math

Humanities

... and beyond

How do you find the values of the six trigonometric functions given $tan θ = - \frac{15}{8}$ $tantheta=-15/8$ and $sin θ < 0$ $sintheta<0$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find the values of the six trigonometric functions given tantheta=-15/8tanθ=−158tantheta=-15/8 and sintheta<0sinθ<0sintheta<0?

1 Answer

Explanation:

Related questions

Impact of this question

How do you find the values of the six trigonometric functions given $tan θ = - \frac{15}{8}$ $tantheta=-15/8$ and $sin θ < 0$ $sintheta<0$ ?