alleryStart learning →How many solutions does 2 sin^2 t - 1 = 0 have on the interval from 0 to 2 pi?
ATwo solutions
BThree solutions
CFour solutions
DSix solutions
Answer & Solution
Correct answer: C. Four solutions
1. Isolate the square: 2 sin^2 t = 1, so sin^2 t = 1/2.
2. The square root property gives sin t = plus or minus 1 / sqrt(2), that is plus or minus sqrt(2)/2.
3. The positive value gives the quadrant I and quadrant II angles pi/4 and 3 pi/4.
4. The negative value gives the quadrant III and quadrant IV angles 5 pi/4 and 7 pi/4.
5. That is four solutions in total, and answering two comes from keeping only the positive root.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.5 Solving Trigonometric Equations_
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