alleryStart learning →Solving sec t = -4 gives t about 1.8235 radians. What is the other solution within one turn?
AAbout 1.3181 radians
BAbout 3.1416 radians
CAbout 5.0000 radians
DAbout 4.4597 radians
Answer & Solution
Correct answer: D. About 4.4597 radians
1. Write sec t = -4 as 1 / cos t = -4, so cos t = -1/4.
2. The inverse cosine of -1/4 is about 1.8235 radians, which lies between pi/2 and pi, so it sits in quadrant II.
3. Cosine is also negative in quadrant III, so a second solution must be found there.
4. The reference angle is pi minus 1.8235, which is about 1.3181.
5. The quadrant III angle is pi plus that reference angle, about 3.1416 + 1.3181.
6. That gives about 4.4597 radians.
7. The figure 1.3181 is only the reference angle, so choosing it stops one step short of the answer.
_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.