9709 · 1.5
Trigonometry flashcards
Revision flashcards for Cambridge 9709 Trigonometry (syllabus 1.5). Flip, recall, then mark a real past-paper question.
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What is the definition of one radian?
One radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius of the circle.
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How do you convert from degrees to radians?
Multiply the angle in degrees by $π/180$. For example, $90° = 90 \times \frac{\pi}{180} = \frac{\pi}{2}$ radians.
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How do you convert from radians to degrees?
Multiply the angle in radians by $180/π$. For example, $\frac{\pi}{3} \text{ rad} = \frac{pi}{3} \times \frac{180}{\pi} = 60°$.
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On the unit circle, what are $\cos \theta$ and $\sin \theta$ in terms of coordinates $(x, y)$?
For a point $P(x, y)$ on the unit circle at angle $\theta$, $\cos \theta = x$ and $\sin \theta = y$.
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What is the fundamental Pythagorean identity in trigonometry?
$\sin^2 \theta + \cos^2 \theta \equiv 1$. This is true for all values of $\theta$.
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How is $\tan \theta$ related to $\sin \theta$ and $\cos \theta$?
$\tan \theta \equiv \frac{\sin \theta}{\cos \theta}$. This identity is undefined when $\cos \theta = 0$.
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What are the exact values of $\sin(\pi/6)$, $\cos(\pi/6)$, and $\tan(\pi/6)$?
$\sin(\pi/6) = 1/2$, $\cos(\pi/6) = \sqrt{3}/2$, $\tan(\pi/6) = 1/\sqrt{3}$.
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What are the exact values for the angle $\pi/4$?
$\sin(\pi/4) = 1/\sqrt{2}$, $\cos(\pi/4) = 1/\sqrt{2}$, $\tan(\pi/4) = 1$.
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What is the period of the graphs $y = \sin x$ and $y = \cos x$?
The period is $2\pi$ radians or $360°$. The graphs repeat every $2\pi$ interval.
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What is the period of the graph $y = \tan x$?
The period is $\pi$ radians or $180°$. It repeats more frequently than sine or cosine.
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Common Mistake: Forgetting calculator mode.
If an exam question involves $\pi$ or specifies a range in terms of $\pi$ (e.g., $0 \le x \le 2\pi$), your calculator MUST be in Radians (RAD) mode. Otherwise, use Degrees (DEG) mode.
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What does the CAST diagram help you remember?
It shows which trigonometric functions are positive in each quadrant. Q1 (All), Q2 (Sine), Q3 (Tangent), Q4 (Cosine).