TS EAMCET Trigonometry: Trigonometric Equations — practice questions
53 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice TS 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 product 2 sin A cos B equalsThe 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?