Trigonometry — Flashcards
Maharashtra Board · Class 9 · Mathematics
22 flashcards for Trigonometry (Maharashtra Board Class 9 Mathematics) to test yourself on key terms and facts.
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What is trigonometry and what does the word mean?
Answer
Trigonometry is a branch of mathematics used to find unknown distances and heights. The word comes from three Greek words: 'Tri' (three), 'gona' (sides), and 'metron' (measurements). It literally mean…
In a right-angled triangle ABC with right angle at B, identify the hypotenuse and the sides opposite and adjacent to angle A.
Answer
Hypotenuse: AC (side opposite to the right angle) Side opposite to ∠A: BC Side adjacent to ∠A: AB Note: The hypotenuse is always the longest side in a right triangle.
State the Pythagoras theorem for a right-angled triangle.
Answer
In a right-angled triangle with hypotenuse 'c' and other two sides 'a' and 'b': c² = a² + b² The square of the hypotenuse equals the sum of squares of the other two sides.
What is the sine ratio (sin θ) of an angle θ in a right triangle?
Answer
sin θ = opposite side / hypotenuse The sine of an angle is the ratio of the length of the side opposite to the angle to the length of the hypotenuse.
What is the cosine ratio (cos θ) of an angle θ in a right triangle?
Answer
cos θ = adjacent side / hypotenuse The cosine of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
What is the tangent ratio (tan θ) of an angle θ in a right triangle?
Answer
tan θ = opposite side / adjacent side The tangent of an angle is the ratio of the length of the side opposite to the angle to the length of the side adjacent to the angle.
State the complementary angle relations for sine and cosine.
Answer
sin θ = cos (90° - θ) cos θ = sin (90° - θ) The sine of an angle equals the cosine of its complement, and vice versa.
Express tan θ in terms of sin θ and cos θ.
Answer
tan θ = sin θ / cos θ This relationship comes from the definitions: tan θ = opposite/adjacent sin θ/cos θ = (opposite/hypotenuse)/(adjacent/hypotenuse) = opposite/adjacent…
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