There is no difference in meaning between the two. It is usually spelled in lowercase, though (arc tan, or arctan).
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1 because tan(5 pi / 4) = 1
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
The arc-tangent of 0.07, often written as (\tan^{-1}(0.07)), is the angle whose tangent is 0.07. In degrees, this value is approximately 4.0 degrees, while in radians, it is about 0.0698 radians. This function is commonly used in trigonometry to find angles corresponding to specific tangent values.
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
Sin = Opposite/Hypotenuse, tan = Opposite/Adjacent