Trigonometry

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Trigonometry is a branch of mathematics that studies the relationship between the sides and angles of triangles. It helps us measure heights, distances, and slopes using the properties of triangles, p

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For angle A: • Hypotenuse (AC) - side opposite to the right angle • Opposite side (BC) - side opposite to angle A • Adjacent side (AB) - side next to angle A (not hypotenuse)

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sin A = Opposite side / Hypotenuse In triangle ABC (right angle at B): sin A = BC/AC This ratio is constant for a given angle A in all similar right triangles.

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cos A = Adjacent side / Hypotenuse In triangle ABC (right angle at B): cos A = AB/AC This ratio remains constant for angle A across all similar right triangles.

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tan A = Opposite side / Adjacent side In triangle ABC (right angle at B): tan A = BC/AB Alternatively: tan A = sin A / cos A

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The three reciprocal ratios are: • cosec A = 1/sin A = Hypotenuse/Opposite side • sec A = 1/cos A = Hypotenuse/Adjacent side • cot A = 1/tan A = Adjacent side/Opposite side

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For 45° (from isosceles right triangle): • sin 45° = 1/√2 • cos 45° = 1/√2 • tan 45° = 1 Note: sin 45° = cos 45° because in an isosceles right triangle, opposite and adjacent sides are equal.

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For 30° (from equilateral triangle): • sin 30° = 1/2 • cos 30° = √3/2 • tan 30° = 1/√3 These values come from dividing an equilateral triangle by its altitude.