Trigonometry identities

[Monokuro]

Solve for 0 ≤ x ≤ 360
1. √2sinx+1=0
2. sin²θ+sinθ=0
3. cos²θ=1-2sin²θ

The answers are as follows:
1. x=225,315
2. x=0,180,270,360
3. x= 0,180,360

How do i get these answers?
thanks

 

[HallsofIvy]

Solve for 0 ≤ x ≤ 360
1. √2sinx+1=0
2. sin²θ+sinθ=0
3. cos²θ=1-2sin²θ

The answers are as follows:
1. x=225,315
2. x=0,180,270,360
3. x= 0,180,360

How do i get these answers?
thanks

1) If the equation were \(\displaystyle \sqrt{2}x+ 1= 0\), could you solve it?

2) If the equation were \(\displaystyle x^2+ x= 0\), could you solve it?

3) I presume you know that \(\displaystyle sin^2(\theta)+ cos^2(\theta)= 1\) so that \(\displaystyle cos^2(\theta)= 1- sin^2(\theta)\). You can use that to write the equation as \(\displaystyle 1- sin^2(\theta)= 1- 2sin^2(\theta)\). If the equation were \(\displaystyle 1- x^2= 1- 2x^2\), could you solve it?

 

[Quaid]

How do i get these answers?

Use basic algebra and basic trigonometry.

Have you studied any algebra or trigonometry, yet?

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