Linear Trigonometric Equations (AQA A-Level Mathematics): Quizzes

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Linear Trigonometric Equations
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What is the period of the tangent function?

180180^\circ or π\pi radians

In which quadrants is sine positive?

First and second quadrants

In which quadrants is cosine negative?

Second and third quadrants

In which quadrants is sine negative?

Third and fourth quadrants

What are the solutions to tanθ=1\tan \theta = 1 for 0θ3600^\circ \leq \theta \leq 360^\circ?

45,22545^\circ, 225^\circ

What is the general solution for tanθ=k\tan \theta = k?

θ=tan1(k)+180n\theta = \tan^{-1}(k) + 180^\circ n

When solving cos(2x)=0.2\cos(2x) = 0.2 for 0x3600 \leq x \leq 360, what are the limits for 2x2x?

02x7200 \leq 2x \leq 720

When solving tan(3x)\tan(3x) with 180x180-180 \leq x \leq 180, what limits should be used for 3x3x?

5403x540-540 \leq 3x \leq 540

Why do trigonometric equations typically have an infinite number of solutions?

Due to the periodic nature of trig functions

What is the first step in solving linear trigonometric equations?

Isolate the trigonometric function

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