If 0 degrees is greater or less than theta greater than 360 degrees, find all values of theta when csc theta equals 2 squared
+33653 Find θ in the range 0≤θ<360° when csc θ = 22 (or csc θ = 4)
csc is 1/sin, so sin θ = 1/4
θ = sin-1(1/4)
$${\mathtt{theta}} = \underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{1}}}{{\mathtt{4}}}}\right)} \Rightarrow {\mathtt{theta}} = {\mathtt{14.477\: \!512\: \!185\: \!93^{\circ}}}$$
θ ≈ 14.5° This is the value within the first quadrant.
sin θ is also positive in the third quadrant, so another approximate value for θ is 180° - 14.5° = 165.5°
+33653 Find θ in the range 0≤θ<360° when csc θ = 22 (or csc θ = 4)
csc is 1/sin, so sin θ = 1/4
θ = sin-1(1/4)
$${\mathtt{theta}} = \underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{1}}}{{\mathtt{4}}}}\right)} \Rightarrow {\mathtt{theta}} = {\mathtt{14.477\: \!512\: \!185\: \!93^{\circ}}}$$
θ ≈ 14.5° This is the value within the first quadrant.
sin θ is also positive in the third quadrant, so another approximate value for θ is 180° - 14.5° = 165.5°
