Question #7ce5f

Question

1125 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-11T19:40:34

For part a. see below.

Given: $sin θ = - \frac{5}{13}$ $sin theta = -5/13$ and $\frac{3 π}{2} < θ < 2 π$ $(3pi)/2 < theta < 2pi$

We know that ${sin}^{2} θ + {cos}^{θ} = 1$ $sin^2theta+cos^theta=1$ for all $θ$ $theta$

Since $\frac{3 π}{2} < θ < 2 π$ $(3pi)/2 < theta < 2pi$ , we see that $cos θ > 0$ $cos theta > 0$

Therefore,

$cos θ = \sqrt{1 - {sin}^{2} θ} = \sqrt{\frac{144}{169}} = \frac{12}{13}$ $costheta = sqrt(1-sin^2theta) = sqrt (144/169) = 12/13$

Now we have

$sin θ = - \frac{5}{13}$ $sin theta = -5/13$ and $cos θ = \frac{12}{13}$ $costheta = 12/13$

The other values can be found using these two.

$tan θ = \frac{sin θ}{cos θ} = - \frac{5}{12}$ $tan theta = sintheta/costheta = -5/12$

$csc θ = \frac{1}{sin θ} = - \frac{13}{5}$ $csc theta = 1/sintheta = -13/5$

$sec θ = \frac{1}{cos θ} = \frac{13}{12}$ $sectheta = 1/costheta = 13/12$

$cot θ = \frac{cos θ}{sin θ} = - \frac{12}{5}$ $cot theta = costheta/sintheta = -12/5$