Trigonometric Functions - II — Flashcards
NIOS · Class 12 · Mathematics
25 flashcards for Trigonometric Functions - II (NIOS Class 12 Mathematics) to test yourself on key terms and facts.
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Find sin(5π/12) given that sin(π/4) = 1/√2 and sin(π/6) = 1/2
Answer
Step 1: Express 5π/12 as a sum: 5π/12 = π/4 + π/6 Step 2: Apply addition formula: sin(A+B) = sin A cos B + cos A sin B Step 3: sin(5π/12) = sin(π/4)cos(π/6) + cos(π/4)sin(π/6) Step 4: Substitute value…
Calculate cos(π/12) using the addition formula for cosine
Answer
Step 1: Express π/12 as a difference: π/12 = π/4 - π/6 Step 2: Apply formula: cos(A-B) = cos A cos B + sin A sin B Step 3: cos(π/12) = cos(π/4)cos(π/6) + sin(π/4)sin(π/6) Step 4: Substitute: cos(π/12)…
When do you use the addition formula sin(A+B) = sin A cos B + cos A sin B? Provide a worked example.
Answer
Use this formula when: (1) You need to find the sine of a sum of two angles, (2) You know the individual sine and cosine values of the angles, (3) The combined angle isn't a standard angle. Example: …
Prove that sin(A+B) - sin(A-B) = 2cos A sin B
Answer
Step 1: Write out the addition and subtraction formulas: sin(A+B) = sin A cos B + cos A sin B sin(A-B) = sin A cos B - cos A sin B Step 2: Subtract the second from the first: sin(A+B) - sin(A-B) = (s…
Express 2sin(3θ)cos(2θ) as a sum or difference
Answer
Step 1: Identify the product-to-sum formula: 2sin A cos B = sin(A+B) + sin(A-B) Step 2: Let A = 3θ and B = 2θ Step 3: Apply formula: 2sin(3θ)cos(2θ) = sin(3θ+2θ) + sin(3θ-2θ) Step 4: Simplify: 2sin(3θ…
Express sin(5π/9) + sin(π/9) as a product
Answer
Step 1: Identify the sum-to-product formula: sin C + sin D = 2sin((C+D)/2)cos((C-D)/2) Step 2: Let C = 5π/9 and D = π/9 Step 3: Calculate (C+D)/2: (5π/9 + π/9)/2 = (6π/9)/2 = 6π/18 = π/3 Step 4: Calcu…
Formula for sin(2A). What does each variable represent? Provide an example.
Answer
Formula: sin(2A) = 2sin A cos A Alternative forms: - sin(2A) = 2tan A / (1 + tan²A) Variables: - A = angle (any real number) - sin(2A) = sine of double angle - sin A, cos A = trigonometric functions…
Find cos(2A) in all its forms when cos A = 3/5 (where 0 < A < π/2)
Answer
Step 1: Find sin A using sin²A + cos²A = 1 sin²A = 1 - (3/5)² = 1 - 9/25 = 16/25 sin A = 4/5 (positive since A is in first quadrant) Step 2: Apply cos(2A) = cos²A - sin²A cos(2A) = (3/5)² - (4/5)² = …
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