AP EAMCET Trigonometry: Trigonometric Equations — practice questions
62 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP EAMCET Trigonometry: Trigonometric Equations in the app →Cosine equals 1/2 at which two angles in one full turn?Between 0 and 2π, tan x = 1 is true for which pair?Given cos x = cos α, all possible x areFrom tan x = tan α we conclude thatSolving sin²x = sin²α yieldsWhat does tan²x = tan²α imply for x?The relation sec x = sec α holds exactly whenFor cot x = cot α, the values of x areCount the roots of sin x = 1/2 lying in [0, 2π].Count the zeros of cos x on the interval [0, 4π].Two angles in [0, 2π] satisfy cos x = −1/2. They areList the angles in [0, 2π] where sin x = −1/2.Find x in [0, 2π] for which tan x = √3 (two values).Pick the value in [0, π) that solves tan x = −1.Solve sin x = 1/2 over all reals.What are all real x with tan x = √3?State the full solution set of cos x = −1/2.Solve tan x = −1/√3 completely.Find all x satisfying cos 3x = 0.Solve the equation sin x + cos x = 0.Given sin x = 1/2 and cos x = −√3/2 in [0, 2π], find x.The usual range of principal values of sin⁻¹ x isWhat is the smallest period of the function sin x?Tangent repeats its values after which smallest interval?The function sin 2x has least periodFind the least period of cos(x/2).The expression 1 + tan²x is equal toThe sum sin C + sin D equalsThe multiple-angle formula for sin 3A isThe solutions of sin θ = 1 are π/2, 5π/2, 9π/2 and so on. Consecutive values differ byFor x in [0, 2π), cos x = 1/2 holds at which pair of angles?In the interval [0, 2π), tan x = 1 for which pair of angles?What is the general solution of the equation sin x = 0, with n an integer?If sin x = sin α, the general solution for integer n is which one?If cos x = cos α, then for integer n the general solution is which one?The equation sin²x = sin²α is satisfied for integer n by which set?For integer n, which values of x satisfy sin x = 1?Which pair solves 2cos x + √3 = 0 for x in [0, 2π]?How many solutions does sin x + cos x = 1 have in [0, 2π]?Find all x with sin x + cos x = √2, for integer n.What is the largest value that sin x + cos x can take?How many real values of x satisfy 3 sin x + 4 cos x = 6?Solve sin x = cos x for integer n and give the general solution.What is the sum of all roots of 2cos²x + cos x - 1 = 0 in [0, 2π)?The equation sin x = a has a real solution only when a satisfies what?The principal value of x for sin x = -1/2, taking x in [-π/2, π/2], is what?What is the principal value of the inverse cosine of -1/2?The equation sec x = 2 has which general solution, with n an integer?The double angle sin 2x is equal to which expression?By the Pythagorean identity, sin²θ + cos²θ is equal to what?In which pair of quadrants is the value of tan x negative?The expression a sin x + b cos x can be written as one sine wave of what amplitude?Besides cosine, which other trigonometric function is even?Sine, cosine, cosecant and secant all repeat after which smallest common period?Which function has vertical asymptotes at every integer multiple of π?Which identity correctly shifts sine by a quarter turn?Which Danish mathematician introduced the terms tangent and secant in 1583?Which scholar proved in 1682 that sin x is not an algebraic function of x?A general periodic function can be written as a sum of sine and cosine waves. What is this expansion called?The zeros of the sine function are all integer multiples of which number?Which statement about tan(x + kπ) for any integer k is correct?Who introduced the tangent function to Europe in 1467 through trigonometry tables?