If θ is an angle in standard position and its terminal side passes through the point ( -12, -35), find the exact value of cosecant, thetacscθ in simplest radical form.
Question
If θ is an angle in standard position and its terminal side passes through the point ( -12, -35), find the exact value of cosecant, thetacscθ in simplest radical form.
Solution
First, we need to find the value of r which is the distance from the origin (0,0) to the point (-12, -35). We can use the Pythagorean theorem to find r:
r = sqrt((-12)^2 + (-35)^2) r = sqrt(144 + 1225) r = sqrt(1369) r = 37
The cosecant of an angle in standard position is defined as the ratio of the length of the hypotenuse (r) to the length of the side opposite the angle (y-coordinate), or cscθ = r/y.
So, cscθ = r/y = 37/-35 = -37/35.
Therefore, the exact value of cscθ in simplest radical form is -37/35.
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