alleryStart learning →Which two angles in one full turn satisfy sin t = 1/2?
Api/3 and 2 pi/3
Bpi/6 and 11 pi/6
Cpi/6 and 5 pi/6
Dpi/4 and 3 pi/4
Answer & Solution
Correct answer: C. pi/6 and 5 pi/6
1. Sine equals 1/2 at the reference angle pi/6.
2. Sine is positive in quadrants I and II.
3. The quadrant I angle is pi/6 and the quadrant II angle is pi - pi/6 = 5 pi/6.
4. The pair pi/6 and 11 pi/6 puts one angle in quadrant IV, where sine is negative, so that option fails.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.5 Solving Trigonometric Equations_
Keep practising Trigonometric Identities and Equations
Browse all Trigonometric Identities and Equations questions for B.Sc Mathematics, or explore more Mathematics topics.
Related questions
If a ladder's base is a feet from the wall and its length is 4a feet, how high up the wallSafety rules place a ladder's base 1 foot from the wall for every 4 feet of ladder length.Compared with y = sin t, the graph of y = sin(2t) is which transformation?Solving sin(n t) = c across one turn requires going around the unit circle how many times?Solve cos(2t) = 1/2 on the interval from 0 to 2 pi.Solve 3 cos t + 3 = 2 sin^2 t exactly on the interval from 0 to 2 pi.Solve cos t cos(2t) + sin t sin(2t) = sqrt(3)/2 on the interval from 0 to 2 pi.Solve 2 sin^2 t + sin t = 0 exactly on the interval from 0 to 2 pi.