Mariam A.

asked • 01/23/22

How to solve this?

Solve the following equations in the interval [0,2\pi].

Note: Give the answer as a multiple of \pi. Do not use decimal numbers. The answer should be a fraction or an integer. Note that \pi is already included in the answer so you just have to enter the appropriate multiple. E.g. if the answer is \pi/2 you should enter 1/2. If there is more than one answer enter them separated by commas.

\sin(t)= \frac{\sqrt{2}}{2}

t= ....... \pi

\sin(t)= -\frac{\sqrt{2}}{2}

t= .......\pi

1 Expert Answer

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LEV K. answered • 01/23/22

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4.9 (107)

Mid and High School Math and SAT prep
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For the sin(t) = sqrt(2)/2, you have 45 degrees(pi/4) reference angle. Don't forget also a corresponding angle in the II quadrant (3pi/4)


So, your answer is 1/4 and 3/4


For the second equation you have 45 degree angle in the III and IV quadrant. Could you figure out a fraction?

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Mariam A.

For the second equation will the answer be -1/4 and 5/4?
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01/23/22

LEV K.

tutor
5/4 is correct. But the second one you need to be in the [0,2pi] interval. So you need to add 2pi to -pi/4
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01/23/22

Mariam A.

So, it will be 7/4 and 5/4. Thanks so much for your help.
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01/23/22

LEV K.

tutor
exactly!
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01/23/22

Mariam A.

Thank you, I really appreciate your help.
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01/23/22

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