Solve for \(0 \leq x \leq 360\).
a) \(\sin^2x - \sin x = 0\)
Answer (2)
s i n 2 x − s in x = 0 s in x ( s in x − 1 ) = 0 ⟺ s in x = 0 or s in x − 1 = 0 s in x = 0 ⟺ x = 0 o or x = 18 0 o or x = 36 0 o s in x − 1 = 0 s in x = 1 ⟺ x = 9 0 o A n s w er : x ∈ { 0 o ; 9 0 o ; 18 0 o ; 36 0 o }
To solve the equation sin 2 x − sin x = 0 , we factor it to find sin x ( sin x − 1 ) = 0 . The solutions are x = 0 ∘ , 9 0 ∘ , 18 0 ∘ , and 36 0 ∘ . The complete set of solutions is x ∈ { 0 ∘ ; 9 0 ∘ ; 18 0 ∘ ; 36 0 ∘ } .
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