Trigonometric Functions - I — Flashcards
NIOS · Class 12 · Mathematics
25 flashcards for Trigonometric Functions - I (NIOS Class 12 Mathematics) to test yourself on key terms and facts. Sample: "Convert 90° to radians"
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Convert 90° to radians
Answer
Step 1: Use the conversion formula 1° = π/180 radians Step 2: 90° = 90 × (π/180) radians Step 3: Simplify = 90π/180 = π/2 radians Answer: π/2 radians…
Convert 5π/6 radians to degrees
Answer
Step 1: Use the conversion formula 1 radian = (180/π)° Step 2: 5π/6 radians = (5π/6) × (180/π) degrees Step 3: Cancel π and simplify = (5 × 180)/6 = 900/6 Step 4: = 150° Answer: 150°…
Find the angle (in radians) subtended by an arc of length 14 cm at the centre of a circle with radius 7 cm
Answer
Formula: θ = ℓ/r (where θ is in radians, ℓ is arc length, r is radius) Step 1: Given ℓ = 14 cm, r = 7 cm Step 2: θ = 14/7 = 2 radians Answer: 2 radians Note: The formula ℓ = rθ is only valid when θ is…
A railroad curve turns through 60° in a distance of 200 m. What should be the radius of the circular track?
Answer
Step 1: Convert 60° to radians: 60° = 60 × (π/180) = π/3 radians Step 2: Use formula r = ℓ/θ Step 3: r = 200 ÷ (π/3) = 200 × (3/π) = 600/π meters Step 4: r ≈ 600/3.14159 ≈ 190.99 m ≈ 191 m Answer: 600…
A train travels at 60 km/hour on a circular track. Through what angle (in radians) does it turn in 20 seconds if the track radius is 5/6 km?
Answer
Step 1: Convert speed to the same units - 60 km/h = 60,000 m/h Step 2: Distance covered in 20 seconds = (60 × 20)/(60 × 60) = 1200/3600 = 1/3 km Step 3: Use θ = ℓ/r formula Step 4: θ = (1/3) ÷ (5/6) =…
Determine the sign of sin(7π/18)
Answer
Step 1: Determine which quadrant 7π/18 lies in Step 2: Convert to decimal: 7π/18 ≈ 7(3.14159)/18 ≈ 1.22 radians Step 3: Compare with quadrant boundaries: First quadrant is 0 to π/2 ≈ 1.571 Step 4: Sin…
What is the sign of tan(5π/9)?
Answer
Step 1: Convert 5π/9 to decimal: 5π/9 ≈ 1.745 radians Step 2: Find quadrant boundaries - Second quadrant: π/2 ≈ 1.571 to π ≈ 3.142 Step 3: Since 1.571 < 1.745 < 3.142, the angle is in the second quadr…
If a point P on the unit circle has coordinates (3/5, 4/5), find sin θ and cos θ
Answer
Step 1: Recall that for a point (x, y) on the unit circle, cos θ = x and sin θ = y Step 2: Given coordinates are (3/5, 4/5) Step 3: Therefore, cos θ = 3/5 = 0.6 Step 4: And sin θ = 4/5 = 0.8 Step 5: V…
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