How do you find the remaining trigonometric functions of $θ$ $theta$ given $sec θ \equiv \frac{13}{5}$ $sectheta-=13/5$ and $sin θ < 0$ $sintheta<0$ ?

Question

How do you find the remaining trigonometric functions of $θ$ $theta$ given $sec θ \equiv \frac{13}{5}$ $sectheta-=13/5$ and $sin θ < 0$ $sintheta<0$ ?

1 Answer

Impact of this question

3562 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-18T07:53:28

$see explanation$ $"see explanation"$

Explanation:

$since sin θ < 0 this indicates that θ is in the$ $"since "sintheta<0" this indicates that "theta" is in the"$
$the third or fourth quadrants$ $"the third or fourth quadrants"$

$∙ x cos θ = \frac{1}{sec θ} = \frac{1}{\frac{13}{5}} = \frac{5}{13}$ $•color(white)(x)costheta=1/sectheta=1/(13/5)=5/13$

$∙ x sin θ = \pm \sqrt{1 - {cos}^{2} θ}$ $•color(white)(x)sintheta=+-sqrt(1-cos^2theta)$

$\Rightarrow sin θ = - \sqrt{1 - {(\frac{5}{13})}^{2}}$ $rArrsintheta=-sqrt(1-(5/13)^2)$

$\Rightarrow sin θ = - \sqrt{\frac{144}{169}} = - \frac{12}{13}$ $color(white)(rArrsintheta)=-sqrt(144/169)=-12/13$

$∙ x csc θ = \frac{1}{sin θ} = \frac{1}{- \frac{12}{13}} = - \frac{13}{12}$ $•color(white)(x)csctheta=1/sintheta=1/(-12/13)=-13/12$

$∙ x tan θ = \frac{sin θ}{cos θ} = \frac{- \frac{12}{13}}{\frac{5}{13}} = - \frac{12}{5}$ $•color(white)(x)tantheta=sintheta/costheta=(-12/13)/(5/13)=-12/5$

$∙ x cot θ = \frac{1}{tan θ} = \frac{1}{- \frac{12}{5}} = - \frac{5}{12}$ $•color(white)(x)cottheta=1/tantheta=1/(-12/5)=-5/12$

$θ is in the fourth quadrant$ $theta" is in the fourth quadrant"$

Science

Math

Humanities

... and beyond

How do you find the remaining trigonometric functions of $θ$ $theta$ given $sec θ \equiv \frac{13}{5}$ $sectheta-=13/5$ 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 remaining trigonometric functions of θtheta given secθ≡135sectheta-=13/5 and sinθ<0sintheta<0?

1 Answer

Explanation:

Related questions

Impact of this question

How do you find the remaining trigonometric functions of $θ$ $theta$ given $sec θ \equiv \frac{13}{5}$ $sectheta-=13/5$ and $sin θ < 0$ $sintheta<0$ ?