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Please help!!!!!!! (100 points!!!!)

How many solutions exist for the equation cos 2θ − sin^2 θ = 0 on the interval [0, 360°)?

3
2
1
0

Respuesta :

fieryanswererft

Answer:

There lies 2 solutions.

Step-by-step explanation:

[tex]cos\:2x\:-\:sin^2\:x\:=\:0\:[/tex]

rewrite the expression:

[tex]\cos ^2\left(x\right)-2\sin ^2\left(x\right)=0[/tex]

Factor the expression:

[tex]\left(\cos \left(x\right)+\sqrt{2}\sin \left(x\right)\right)\left(\cos \left(x\right)-\sqrt{2}\sin \left(x\right)\right)=0[/tex]

solve them separately:

[tex]\cos \left(x\right)+\sqrt{2}\sin \left(x\right)=0\quad \ \ or \ \ \cos \left(x\right)-\sqrt{2}\sin \left(x\right)=0[/tex]  

final answer:

[tex]35.26438^{\circ \:}[/tex] , [tex]215.3^{\circ \:}[/tex]

mathstudent55

Answer:

4 solution

Step-by-step explanation:

cos 2θ − sin^2 θ = 0

Use trig identity cos 2θ = 1 - 2sin² θ

cos 2θ − sin^2 θ = 0

1 - 2sin² θ − sin^2 θ = 0

-3sin² θ = -1

sin² θ = 1/3

sin θ = ±√(1/3)

The reference angle is 35.26°.

Since the interval is [0, 360°), there are 4 solutions:

35.26°, 144.74°, 215.26°, 324.74°

There are 4 solutions.

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