Pearson Algebra 2 Common Core, 2011
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Pearson Algebra 2 Common Core, 2011 View details
2. Solving Trigonometric Equations Using Inverses
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Exercise 71 Page 918

The range of a standard, non-transformed sine function is between and in the interval

D

Practice makes perfect
Given we want to determine the conditions for and so that the function to has exactly two solutions in the interval To do so, let's first isolate using the Division Property of Equality.
Now we can see that we are actually looking for values of a standard, non-transformed sine function. The range of a sine function is between and
Graph of a Sine Function

Because we want to only consider the values of that are equal to two different values of we need to look at every point in this interval except the maximum and the minimum, and For both and there is only one possible value of

Graph of a Sine Function
Since the maximum and minimum values would not have two solutions in the given interval, we know that the values of must be between, and not including, and
Now, we can substitute for in this inequality.
Finally, using the Multiplication Property of Inequality, we can multiply each side by We were given that is positive so we do not need to worry about flipping the inequality sign.
Therefore, if is less than but greater than the given function has exactly two solutions. This corresponds to option D.