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

`\sin 253.740^(\textdegree) = -(24)/(25) = -0.960`

`\cos 253.740^(\textdegree) = -(7)/(25) = -0.280`

`\tan 253.340^(\textdegree) = (24)/(7) = 3.429`

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((24)/(7) \right)`

`\theta \approx 253.740^(\textdegree)`

The values of the trigonometrical functions are computed below:

`\sin 253.740^(\textdegree) = -(24)/(25) = -0.960`

`\cos 253.740^(\textdegree) = -(7)/(25) = -0.280`

`\tan 253.340^(\textdegree) = (24)/(7) = 3.429`