Question

The point (−7, -24) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.

Answer 1

Answer:

$\sin 253.740^{\textdegree} = -\frac{24}{25} = -0.960$

$\cos 253.740^{\textdegree} = -\frac{7}{25} = -0.280$

$\tan 253.340^{\textdegree} = \frac{24}{7} = 3.429$

Step-by-step explanation:

The point is in the 3rd Quadrant of the Cartesian Plane. Therefore, angle must be between 180° and 270° with respect to the horizontal.

The angle is:

$\theta = 180^{\textdegree}+\tan^{-1}\left(\frac{24}{7} \right)$

$\theta \approx 253.740^{\textdegree}$

The values of the trigonometrical functions are computed below:

$\sin 253.740^{\textdegree} = -\frac{24}{25} = -0.960$

$\cos 253.740^{\textdegree} = -\frac{7}{25} = -0.280$

$\tan 253.340^{\textdegree} = \frac{24}{7} = 3.429$