Trigonometry — NCERT Class 10: 25 flashcards
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1. What is $\sin A$ in a right triangle?
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$\sin A = \dfrac{\text{opposite}}{\text{hypotenuse}}$
2. What is $\cos A$ in a right triangle?
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$\cos A = \dfrac{\text{adjacent}}{\text{hypotenuse}}$
3. What is $\tan A$ in a right triangle?
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$\tan A = \dfrac{\text{opposite}}{\text{adjacent}}$
4. Which side is always the hypotenuse?
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The side opposite the right angle — the longest side.
5. How are opposite and adjacent defined?
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Relative to the angle being used, not to a fixed corner.
6. Write the three reciprocal ratios.
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$\csc A = \frac{1}{\sin A}$, $\sec A = \frac{1}{\cos A}$, $\cot A = \frac{1}{\tan A}$
7. Why do trigonometric ratios depend only on the angle?
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Because right triangles with the same acute angle are similar, so side ratios are equal.
8. State the identity $\sin^2 A + \cos^2 A = 1$.
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For any acute angle $A$, $\sin^2 A + \cos^2 A = 1$.
9. State the identity $1 + \tan^2 A = \sec^2 A$.
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$1 + \tan^2 A = \sec^2 A$ for any acute angle $A$.
10. State the identity $1 + \cot^2 A = \csc^2 A$.
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$1 + \cot^2 A = \csc^2 A$ for any acute angle $A$.
11. What is $\sin 30^\circ$?
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$\sin 30^\circ = \dfrac{1}{2}$
12. What is $\cos 60^\circ$?
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$\cos 60^\circ = \dfrac{1}{2}$
13. What is $\tan 45^\circ$?
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$\tan 45^\circ = 1$
14. What is $\sin 45^\circ$?
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$\sin 45^\circ = \dfrac{1}{\sqrt{2}}$
15. What is $\tan 90^\circ$?
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Not defined (since $\cos 90^\circ = 0$).
16. What is the angle of elevation?
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The angle measured upward from the horizontal to the line of sight.
17. What is the angle of depression?
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The angle measured downward from the horizontal to the line of sight.
18. What does $\sin^2 A$ mean?
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$(\sin A)^2$ — square the ratio, not the angle.
19. In triangle $ABC$ right-angled at $B$, what is $\sin A$?
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$\sin A = \dfrac{BC}{AC}$
20. In the same triangle, why is $\sin A = \cos C$?
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Because opposite and adjacent swap roles for the two acute angles.
21. For acute $A$, what is the range of $\sin A$ and $\cos A$?
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$0 < \sin A < 1$ and $0 < \cos A < 1$.
22. How do you choose which ratio to use in a problem?
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Identify which two sides the problem links: opposite/hypotenuse → $\sin$; adjacent/hypotenuse → $\cos$; opposite/adjacent → $\tan$.
23. What are the four steps to solve a trigonometry problem?
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Draw and label, choose the ratio, substitute values, solve and check.
24. Is $\sin(A+B) = \sin A + \sin B$?
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No — trigonometric functions do not distribute over addition.
25. What is $\cos 0^\circ$ and $\cos 90^\circ$?
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$\cos 0^\circ = 1$ and $\cos 90^\circ = 0$.
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