Introduction to Trigonometry — Flashcards
Gujarat Board · Class 10 · Mathematics
26 flashcards for Introduction to Trigonometry (Gujarat Board Class 10 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 the study of relationships between the sides and angles of a triangle. The word 'trigonometry' comes from Greek words: 'tri' (three), 'gon' (sides), and 'metron' (measure). It literall…
In a right triangle ABC with right angle at B, identify the hypotenuse, opposite side, and adjacent side with respect to angle A.
Answer
With respect to angle A: Hypotenuse = AC (longest side, opposite to right angle), Opposite side = BC (side facing angle A), Adjacent side = AB (side next to angle A, forming the angle).
Write the formula for sine of angle A in a right triangle.
Answer
sin A = (side opposite to angle A)/(hypotenuse) = BC/AC. Remember: sine = opposite/hypotenuse.
Write the formula for cosine of angle A in a right triangle.
Answer
cos A = (side adjacent to angle A)/(hypotenuse) = AB/AC. Remember: cosine = adjacent/hypotenuse.
Write the formula for tangent of angle A in a right triangle.
Answer
tan A = (side opposite to angle A)/(side adjacent to angle A) = BC/AB. Remember: tangent = opposite/adjacent. Also, tan A = sin A/cos A.
Write the formulas for cosecant, secant, and cotangent of angle A.
Answer
cosec A = 1/sin A = AC/BC, sec A = 1/cos A = AC/AB, cot A = 1/tan A = AB/BC. These are reciprocals of sin A, cos A, and tan A respectively.
Why do trigonometric ratios remain constant for a given angle regardless of the size of the triangle?
Answer
Trigonometric ratios remain constant because when triangles have the same angles, they are similar triangles. In similar triangles, the ratios of corresponding sides are equal, so the trigonometric ra…
Find sin 45°, cos 45°, and tan 45°.
Answer
sin 45° = 1/√2, cos 45° = 1/√2, tan 45° = 1. In a 45-45-90 triangle, the two legs are equal, making opposite and adjacent sides equal to the hypotenuse divided by √2.
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