Trigonometric Ratios Of Some Special Angles
NIOS · Class 10 · Maths
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See them allSolve: In a right triangle, if one acute angle is 45° and one side adjacent to it is a units, find the hypotenuse.
Answer
Step 1: For 45°, the two legs are equal, so the other leg is also a units. Step 2: Use Pythagoras theorem: hypotenuse^2 = a^2 + a^2 = 2a^2. Step 3: Hypotenuse = sqrt(2)a. Answer: The hypotenuse is sqr…
Find sin 45°, cos 45°, tan 45°, cosec 45°, sec 45°, and cot 45°.
Answer
Step 1: In a 45°-45°-90° triangle, both legs are equal and the hypotenuse is sqrt(2) times one leg. Step 2: sin 45° = 1/sqrt(2). Step 3: cos 45° = 1/sqrt(2). Step 4: tan 45° = 1. Step 5: cosec 45° = s…
Solve: In the 30° construction, if PM = a units, find OP and OM.
Answer
Step 1: In the 30° construction, the triangle formed becomes equilateral with side 2a. Step 2: Therefore OP = 2a units. Step 3: Use Pythagoras theorem in the right triangle: OP^2 = PM^2 + OM^2. Step 4…
Find sin 30°, cos 30°, tan 30°, cosec 30°, sec 30°, and cot 30°.
Answer
Step 1: Use the 30° special triangle values. Step 2: sin 30° = 1/2. Step 3: cos 30° = sqrt(3)/2. Step 4: tan 30° = 1/sqrt(3). Step 5: cosec 30° = 2. Step 6: sec 30° = 2/sqrt(3). Step 7: cot 30° = sqrt…
Solve: In the 60° construction, if OM = a units, find PM and OP.
Answer
Step 1: In the 60° construction, the triangle formed becomes equilateral with side 2a. Step 2: Therefore OP = 2a units. Step 3: Use Pythagoras theorem in the right triangle: OP^2 = OM^2 + PM^2. Step 4…
Find sin 60°, cos 60°, tan 60°, cosec 60°, sec 60°, and cot 60°.
Answer
Step 1: Use the 60° special triangle values. Step 2: sin 60° = sqrt(3)/2. Step 3: cos 60° = 1/2. Step 4: tan 60° = sqrt(3). Step 5: cosec 60° = 2/sqrt(3). Step 6: sec 60° = 2. Step 7: cot 60° = 1/sqrt…
Evaluate: tan^2 60° - sin^2 30°
Answer
Step 1: tan 60° = sqrt(3), so tan^2 60° = 3. Step 2: sin 30° = 1/2, so sin^2 30° = 1/4. Step 3: Subtract: 3 - 1/4 = 11/4. Answer: 11/4.
Evaluate: cot^2 30° sec^2 45° + cosec^2 45° cos 60°
Answer
Step 1: cot 30° = sqrt(3), so cot^2 30° = 3. Step 2: sec 45° = sqrt(2), so sec^2 45° = 2. Step 3: cosec 45° = sqrt(2), so cosec^2 45° = 2. Step 4: cos 60° = 1/2. Step 5: Compute: (3)(2) + (2)(1/2) = 6…
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