MCB3 group; Homework due on 03-25-2017 Formula of Addition (1) sin (a + b) = sin (a) * cos (b) + sin (b) * cos (a) - this equation is always true; it is a fundamental formula, and we will prove it sometime. T1 Based on the identity (1) prove the following identities sin (a - b) = sin (a) * cos (b) - sin (b) * cos (a) We did this in the class; make sure you understand the way we use the fact that sin(a) is an odd function and cos(a) is an even function. We also use the definition of subtraction (it is addition of opposite). T2 Using formula (1) prove identity (Hint: in formula (1) set b = a) -------------- T3 sin (2*a) = 2 * sin(a) * cos(a) Solve equation: sin (x) = sin (2*x) , if 0 ≤ x ≤ 2* π T4 If 0 ≤ x ≤ π; cos(x) = 3/5; how much is sin(2*x) T5 If sin(35°) = K, then how much is sin (70°), and cos (70°) in terms of K? T6* sin (2*t) = 24/25; and How much is cos (t)? T7 Prove identity T8 Prove identity 0 < x < π/2 ; T9* Compute Q1 Nick read 100 pages at the rate of 50 pages an hour in the morning; in the evening he was reading 100 pages at the rate 40 pages per hour. What was his average for reading per hour for the whole day? Q2 A farmer had to plough the field in 5 days. However, he increased his productivity by 2 acres a day, and finished the job 1 day earlier than planned. What is the area of his field in acres? Q3 Graph of equation x2 + y2 = 169 is a circle. Which of the following points is outside the circle? A) B) C) D) E) (5, 12) (9, 9) (11, 5) (10, 10) None of the above. Solve inequalities I1 -x2 + 12*x + 28 I2 3 / (x + 3) I3 x42 > < 9 * x45 1/3 > 0

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