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What is the value of x in Arc tanx 5pidivided by 4?
1 because tan(5 pi / 4) = 1
What are the alternative ways of finding the length of the hypotenuse of a right angle triangle without using Pythagoras theorem?
The least accurate is to draw the triangle and then measuring it. Alternatively you can use trigonometric ratios: tan = opposite/adjacent sin = opposite/hypotenuse → hypotenuse = opposite/sin cos = adjacent/hypotenuse → hypotenuse = adjacent/cos Using the tangent ration one of the non-right angles of the triangle can be found. Then using either the sine or cosine ratio the hypotenuse can be found. eg if the two "legs" are 1 cm and √2 cm, then: The angle at the end of the √2 cm side is: arc tan(1/√2) = 30° Then the hypotenuse is: 1 cm / sin (arc tan(1/√2)) = 1 cm / ½ = 2 cm. or √2 / cos (arc tan(1/√2)) = √2 / (1/√2) = √2 × √2 = 2. eg if the two "legs" are 3 cm and 4 cm, then: The angle at the end of the 4 cm side is: arc tan ¾ ≈ 36.87° The the hypotenuse is: 3 / sin(arc tan ¾) = 3/0.6 = 5 or 4 / cos(arc tan ¾) = 3/0.8 = 5
What are the functions and classification in calculus?
1.4 Classification Of FunctionsAnalytically represented functions are either Elementary or Non-elementary.The basic elementary functions are :1) Power function :y = xm , m ÎR2) Exponential function :y = ax , a > 0 but a ¹ 13) Logarithmic function :y = log ax , a > 0, a ¹ 1 and x > 04) Trigonometric functions :y = sin x, y = cos x, y = tan x,y = csc x, y = sec x and y = cot x5) Inverse trigonometric functionsy = sin-1 x, y = cos-1x, y = tan-1x,OR y = cot-1x, y = cosec-1x, y = sec-1x.y = arc sin x, y = arc cos x, y = arc tan xy = arc cot x, y = arc csc x and y = arc sec x
What is the difference between sinx and tanx?
Sin = Opposite/Hypotenuse, tan = Opposite/Adjacent
How do you calculate arc length given length of chord and distance of chord to arc through the center?
It is much easier to follow what is below if you have a rough sketch. Suppose the length of the chord is 2x units so that half the chord is x units. Suppose that the distance from the centre of the circle to the arc = y units. Suppose the angle subtended at the centre by the chord is 2k radians. Then the semi-chord and the line from the centre form a right angled triangle with the radius to the end of the chord, and the angle subtended by the semi-chord at the centre is k radians. Now, by Pythagoras the radius, r = sqrt(x2 + y2) units and tan(k) = x/y (or sin(k) = x/r Since both x and y are given, r and k can be calculated. Then arc length = r*k which is a simple multiplication. If you measure angles in degrees, remember that pi radians = 180 degrees.
