alleryStart learning →With sin t = 0.8 and the first angle at about 53.1 degrees, what is the second angle within one turn?
AAbout 126.9 degrees
BAbout 143.1 degrees
CAbout 233.1 degrees
DAbout 306.9 degrees
Answer & Solution
Correct answer: A. About 126.9 degrees
1. The inverse sine of 0.8 is about 0.9273 radians, which is about 53.1 degrees.
2. Sine is positive in quadrants I and II, so a second solution exists in quadrant II.
3. The quadrant II partner is found as 180 degrees minus the reference angle.
4. That gives 180 - 53.1 = 126.9 degrees.
5. Checking, sin 126.9 degrees is about 0.8, as required.
6. The values 233.1 and 306.9 degrees lie in quadrants III and IV, where sine is negative, so neither can satisfy the equation.
_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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