Formula 1:
`\sin\theta=0\Rightarrow\theta=n\pi`.
Example:
(1) Solve `\sin3x=0`.
Given that,
`\sin3x=0`
`\Rightarrow3x=n\pi`
`\Rightarrowx=\frac(n\pi)(3)`.
(2) Solve `2\sin3x\cos3x=0`
Solution: Try yourself.
(3) Solve `\sin2x\cos2x=0`.
Solution: Try yourself.
(4) Solve `\sin^2(\frac(x)(2))=0`.
Solution: Try yourself.
(5) Solve `\sin(\frac(x)(4))\cos(\frac(x)(4))=0`.
Solution: Try yourself.
Formula 2: `\cos\theta=0\Rightarrow\theta=(2n+1)\frac(\pi)(2)`.
Example:
(1) Solve `\cos\5theta=0`.
Solution:
Given that,
`\cos\5theta=0`
`\Rightarrow5\theta=(2n+1)\frac(\pi)(2)`
`\Rightarrow\theta=(2n+1)\frac(\pi)(10)`
(2) Solve `\cos^2\5theta=0`.
Solution: Try yourself.
Formula 3:
`\tan\theta=0\Rightarrow\theta=n\pi`.
Formula 4:
`\sin\theta=\sin\alpha\Rightarrow\theta=n\pi+(-1)^n\alpha`.
Formula 5:
`\cos\theta=\cos\alpha\Rightarrow\theta=(2n\pi\pm\alpha)`.
Formula 6:
`\tan\theta=\tan\alpha\Rightarrow\theta=(n\pi+\alpha)`.
Formula 7:
`\sin\theta=1\Rightarrow\theta=(4n+1)\frac(\pi)(2)`.
Formula 8:
`\cos\theta=1\Rightarrow\theta=2n\pi`.
Formula 9:
`\sin\theta=-1\Rightarrow\theta=(4n-1)\frac(\pi)(2)`.
Formula 10:
`\cos\theta=-1\Rightarrow\theta=(2n\pm1)\pi`.