NDA · Chapter

Trigonometric Equations

The concepts NDA needs, one connected idea at a time.

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\theta = n\pi + (-1)^n\alpha

,

n \in \mathbb{Z}

; no solution when

|\sin\theta|

would exceed

1

Locked

General solutions of cos θ and tan θ

\cos\theta = \cos\alpha

:

\theta = 2n\pi \pm \alpha

;

\tan\theta = \tan\alpha

:

\theta = n\pi + \alpha

Locked

Equations in sin²θ, cos²θ, tan²θ

\sin^2\theta = \sin^2\alpha

(likewise

\cos^2

,

\tan^2

) gives

\theta = n\pi \pm \alpha

; both signs of the root countLocked

Equations that reduce to the standard formsFactorise, use identities or divide out a common ratio to reach

\sin\theta = k

,

\cos\theta = k

or

\tan\theta = k

; don't divide by a factor that can be

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