TS EAPCET (Engineering) Trigonometry: Hyperbolic Functions — practice questions
57 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice TS EAPCET (Engineering) Trigonometry: Hyperbolic Functions in the app →Which expression defines the hyperbolic sine, sinh x?Which formula gives the hyperbolic cosine, cosh x?The hyperbolic tangent tanh x is the ratio of which two functions?For x not equal to 0, coth x is defined as which ratio?The expression 2/(e^x - e^(-x)) represents which hyperbolic function?A sensor reading is scaled by cosh 0. What is the scaling factor?For every real x, cosh^2 x - sinh^2 x is equal to what?The quantity 1 - tanh^2 x simplifies to which function?Which function equals coth^2 x - 1?Adding cosh x and sinh x for any real x gives which result?Subtracting sinh x from cosh x leaves which expression?A model has e^x = 2. What is the value of sinh x?If e^x = 3, then cosh x equals what value?When e^x = 3, what does tanh x evaluate to?A real number x satisfies sinh x = 3/4. What is cosh x?Given cosh x = 5/3 with x > 0, find sinh x.If tanh x = 5/13, what is sech x for positive x?Suppose sinh x = 3/4. Using the double-argument rule, sinh 2x is what?Given tanh x = 1/2, what is tanh 2x?With tanh x = 1/2 and tanh y = 1/3, find tanh(x + y).Evaluate sinh(ln 2).Compute sinh(ln 5), using e^(ln 5) = 5.For x at least 1, arcosh x can be written as which logarithm?Evaluate artanh(1/2) using the logarithmic form of the inverse.What is the exact value of arsinh(3/4)?Find arcosh(5/3) in exact form.What is the slope of the curve y = sinh x at x = 0?The derivative of y = arsinh x is which function?For x greater than 1, d/dx of arcosh x is what?For |x| less than 1, what is the derivative of artanh x?Evaluate the indefinite integral of sinh 2x with respect to x.What is the indefinite integral of tanh x?Find the value of the integral of cosh x from x = 0 to x = ln 2.The integral of 1/√(x² + 1) with respect to x equals which function plus C?In the Taylor series of sinh x about 0, what is the coefficient of x³?Which is the coefficient of x² in the Maclaurin expansion of cosh x?What is the limit of (sinh x)/x as x approaches 0?Find the limit of (cosh x - 1)/x² as x tends to 0.In the series for tanh x near 0, the x³ term has which coefficient?Which of these hyperbolic functions is an even function?A calculator shows tanh 0.5 = 0.462. What is tanh(-0.5)?Over all real x, the values of cosh x fill which range?As x runs over all real numbers, tanh x takes values in which interval?Which circular-function expression equals cosh x?The hyperbolic sine can be obtained from the ordinary sine as which formula?For real x, tanh(ix) equals which expression?For real x, cosh(ix) simplifies to which ordinary trigonometric function?The points (cosh t, sinh t) trace which curve in the plane?A chain hanging freely under gravity takes the shape y = a cosh(x/a). What is this curve called?In special relativity, hyperbolic functions are used to express which kind of transformation?Which function f solves f' = 1 - f² with f(0) = 0?If c' = s and s' = c with s(0) = 0 and c(0) = 1, then s(x) equals what?Which function links circular and hyperbolic functions without using complex numbers?In the complex plane, the hyperbolic tangent and the other derived hyperbolic functions are what kind of functRaising cosh x + sinh x to the third power gives which expression?The sum sinh x + sinh y is the same as 2 sinh((x + y)/2) multiplied by what?The expression (cosh x - 1)/sinh x equals which half-argument value?