Solving Trigonometric Equations — Unit test Answers
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1
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What is the value of 1 − 2sin2(105°)?
A
Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction
B
Negative one-half
C
One-half
D
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
2
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Read the proof.
A
tangent double angle identity
B
tangent sum identityC
tangent double angle identity
D
tangent sum identity3
What is the solution to the trigonometric inequality over the interval radians?
A
0 is less than equal to x and x is less than StartFraction pi over 4 EndFraction
B
and
C
x is greater than StartFraction pi over 4 EndFraction but less than StartFraction 5pi over 4 EndFraction
D
and
4
To solve the trigonometric inequality over the interval radians, Gabby performed the following steps, first simplifying the inequality and then setting both sides equal to y and graphing the equations. Step 1: Step 2: Step 3: Step 4: Step 5: Step 6: In which step did she first make an error, and what was the error?
A
She first made an error in step 3 because she should not have subtracted and added to the right side of the inequality.
B
She first made an error in step 4 because the simplified form of the inequality should have been instead of .
C
She first made an error in step 5 because she did not correctly graph .
D
She first made an error in step 6 because she chose the wrong interval in which the graph of one equation is at or above the graph of the other equation.5
For 0 ≤ x < 2π, which of the following solves 2cos + 1 = 0?
A
Left-brace StartFraction 4 pi Over 3 EndFraction right-brace
B
Left-brace StartFraction 5 pi Over 3 EndFraction right-brace
C
Left-brace StartFraction pi Over 3 EndFraction, StartFraction 2 pi Over 3 EndFraction right-brace
D
Left-brace StartFraction pi Over 3 EndFraction, StartFraction 5 pi Over 3 EndFraction right-brace
6
According to your graphing calculator, what is the approximate solution to the trigonometric inequality over the interval radians?
A
x is greater than equal to 0 but less than 0.7896
B
x is greater than equal to 0 but less than 0.9799
C
x is greater than equal to 0 but less than 0.9870
D
x is greater than equal to 0 but less than 1.2249
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