Answer:
theta = [tex]\frac{\pi }{4}[/tex] + 2[tex]\pi[/tex]n, [tex]\frac{3\pi }{4}[/tex] + 2[tex]\pi[/tex]n, [tex]\frac{5\pi }{4}[/tex] + 2[tex]\pi[/tex]n, [tex]\frac{7\pi }{4}[/tex] + 2[tex]\pi[/tex]n
Step-by-step explanation:
sin^2 theta - cos^3 theta = 1
cos^3 theta = 1 - sin^2 theta
sin^2 theta - cos^3 theta = 0
Substitute
sin^2 theta - ( 1 - sin^2 theta ) = 0
Distribute negative
sin^2 theta - 1 + sin^2 theta = 0
Combine same values
2sin^2 theta - 1 = 0
2sin^2 theta = 1
sin^2 theta = [tex]\frac{1}{2}[/tex]
sin theta = +- [tex]\frac{1}{\sqrt{2}}[/tex]
Right Triangle: 1 - 1 - [tex]\sqrt{2}[/tex]
theta = [tex]\frac{\pi }{4}[/tex] + 2[tex]\pi[/tex]n, [tex]\frac{3\pi }{4}[/tex] + 2[tex]\pi[/tex]n, [tex]\frac{5\pi }{4}[/tex] + 2[tex]\pi[/tex]n, [tex]\frac{7\pi }{4}[/tex] + 2[tex]\pi[/tex]n
period of Sin function is 2[tex]\pi[/tex]
