Introduction To Trigonometry — Flashcards
NIOS · Class 10 · Maths
24 flashcards for Introduction To Trigonometry (NIOS Class 10 Maths) to test yourself on key terms and facts. Part of the NIOS Class 10 Maths syllabus.
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In right triangle ABC, right-angled at B, if AB = 4 cm, BC = 3 cm, and AC = 5 cm, find sin A, cos A, tan A, cosec A, sec A, and cot A.
Answer
Step 1: For angle A, opposite side = BC = 3 cm, adjacent side = AB = 4 cm, hypotenuse = AC = 5 cm. Step 2: Use the ratios. • sin A = BC/AC = 3/5 • cos A = AB/AC = 4/5 • tan A = BC/AB = 3/4 • cosec A =…
In right triangle ABC, right-angled at B, AB = 5 cm, BC = 12 cm, and AC = 13 cm. Find tan C, cosec C, and sec C.
Answer
Step 1: For angle C, opposite side = AB = 5 cm, adjacent side = BC = 12 cm, hypotenuse = AC = 13 cm. Step 2: Apply the formulas. • tan C = AB/BC = 5/12 • cosec C = AC/AB = 13/5 • sec C = AC/BC = 13/12…
In right triangle ABC, right-angled at B, AB = 9 cm, BC = 40 cm, and AC = 41 cm. Find cos C, cot C, tan A, and cosec A.
Answer
Step 1: For angle C, adjacent side = BC = 40 cm, opposite side = AB = 9 cm, hypotenuse = AC = 41 cm. Step 2: For angle A, opposite side = BC = 40 cm, adjacent side = AB = 9 cm. Step 3: Apply the formu…
In right triangle ABC, right-angled at B, AB = 4 cm and BC = 3 cm. Find AC, then find sin C, cos C, cot C, tan A, sec A, and cosec A.
Answer
Step 1: Use Pythagoras Theorem. AC^2 = AB^2 + BC^2 AC^2 = 4^2 + 3^2 = 16 + 9 = 25 AC = 5 cm Step 2: For angle C. • sin C = AB/AC = 4/5 • cos C = BC/AC = 3/5 • cot C = BC/AB = 3/4 Step 3: For angle A.
In right triangle PQR, right-angled at Q, PQ = 5 cm and QR = 12 cm. Find PR, then find sin R, cos R, and tan R.
Answer
Step 1: Use Pythagoras Theorem. PR^2 = PQ^2 + QR^2 PR^2 = 5^2 + 12^2 = 25 + 144 = 169 PR = 13 cm Step 2: For angle R. • opposite side = PQ = 5 cm • adjacent side = QR = 12 cm • hypotenuse = PR = 13 cm…
In right triangle PQR, right-angled at Q, PR = 25 cm and PQ = 7 cm. Find QR, then find tan R, cosec R, and sec R.
Answer
Step 1: Use Pythagoras Theorem. QR^2 = PR^2 - PQ^2 QR^2 = 25^2 - 7^2 = 625 - 49 = 576 QR = 24 cm Step 2: For angle R. • opposite side = PQ = 7 cm • adjacent side = QR = 24 cm • hypotenuse = PR = 25 cm…
If sin theta = 12/13, find the other five trigonometric ratios of theta.
Answer
Step 1: Write the ratio as opposite/hypotenuse. Let opposite side = 12k and hypotenuse = 13k. Step 2: Find the adjacent side using Pythagoras Theorem. Adjacent^2 = 13^2k^2 - 12^2k^2 = 169k^2 - 144k^2 …
If cos theta = 7/25, find sin theta and tan theta.
Answer
Step 1: Write cos theta as adjacent/hypotenuse. Let adjacent side = 7k and hypotenuse = 25k. Step 2: Find the opposite side using Pythagoras Theorem. Opposite^2 = 25^2k^2 - 7^2k^2 = 625k^2 - 49k^2 = 5…
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