Trigonometry and Calculus Problems

Added on 2020-01-23

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1) In a right triangle, the measure of one of the angles is 49° and the hypotenuse has a length of 50 cm. Which of the following is the nearest approximation to the length, in cm, of the leg opposite to this angle?Ans) 32.8 cmWorkingA= 49°Cos 49° = AB/AC0.65 = AB/50AB = 50*0.65605902899AB= 32.8 cm 2) A Cartesian coordinate system specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length. Ans) True3) Convert the Cartesian Coordinates (12, 5) in a right angle triangle to Polar Coordinates. Ans) 13, 22.6^0Working Cartesian (x,y) = polar (r, θ)R = √x2+y2= √122+52= 13Further, θ = Tan-1yx= Tan-1125θ = 22.64. Express 63 degrees 14 minutes and 51 sec in radian form?

Ans) 1.10 radiansWorking Radians = Degree π/ 180 = (63*3.14)/180 = 1.15) What are the three terms used to describe a sinusoidal function?Ans) Period, Sinusoidal Axis and Amplitude

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