Trigonometric Functions
Punjab Board · Class 11 · Mathematics
Flashcards for Trigonometric Functions — Punjab Board Class 11 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Explore the full setConvert 40° 20' to radian measure. (Use π/180 conversion)
Answer
Step 1: Convert minutes to decimal degrees: 40° 20' = 40 + 20/60 = 40 + 1/3 = 121/3 degrees Step 2: Use formula: Radian measure = (π/180) × Degree measure Step 3: Radian measure = (π/180) × (121/3) = …
Convert 6 radians to degree measure. (Use π ≈ 22/7)
Answer
Step 1: Use formula: Degree measure = (180/π) × Radian measure Step 2: Degree measure = (180/π) × 6 = (1080 × 7)/22 = 7560/22 = 343 7/11 degrees Step 3: Convert fractional part to minutes: 7/11 × 60 =…
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
Answer
Step 1: Find revolutions in 1 second: 360 revolutions/minute ÷ 60 seconds = 6 revolutions/second Step 2: Convert revolutions to radians: 1 revolution = 2π radians Step 3: Radians in 1 second = 6 × 2π …
Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm. (Use π = 22/7)
Answer
Step 1: Use the formula θ = l/r where θ is in radians, l is arc length, r is radius Step 2: θ = 22/100 = 0.22 radians = 11/50 radians Step 3: Convert to degrees: Degree measure = (180/π) × (11/50) Ste…
If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, find the ratio of their radii.
Answer
Step 1: Convert angles to radians θ₁ = 65° = (π/180) × 65 = 13π/36 radians θ₂ = 110° = (π/180) × 110 = 22π/36 radians Step 2: Use formula l = rθ. Since arc lengths are equal: l = r₁θ₁ = r₂θ₂ Step 3:…
If sin x = 3/5 and x lies in the second quadrant, find all other five trigonometric functions.
Answer
Step 1: Find cos x using sin²x + cos²x = 1 cos²x = 1 - (3/5)² = 1 - 9/25 = 16/25 cos x = ±4/5 Since x is in second quadrant (where cos is negative): cos x = -4/5 Step 2: Find remaining functions sec …
If cos x = -3/5 and x lies in the third quadrant, find sin x, tan x, and cot x.
Answer
Step 1: Find sin x using sin²x + cos²x = 1 sin²x = 1 - cos²x = 1 - (-3/5)² = 1 - 9/25 = 16/25 sin x = ±4/5 Since x is in third quadrant (where sin is negative): sin x = -4/5 Step 2: Find tan x and co…
Find the value of sin(31π/3). (Hint: Use the periodicity of sine function)
Answer
Step 1: Recognize that sin x has period 2π. We need to subtract multiples of 2π until we get an angle in [0, 2π) Step 2: Express 31π/3 in terms of 2π 31π/3 ÷ 2π = 31π/3 × 1/(2π) = 31/6 = 5 + 1/6 So 3…
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