If sin(theta)= -.1234, find all (theta) in [-4pi,pi] that make this eq true?

[mauro125]

what i have so far:
sin is negative in QIII,QIV
sin^-1(-.1234)=-.1237

0 - .1237 = -.1237
-pi + .1237 = -3.0179
-2pi - .1237 = -6.4069
-3pi + .1237 = -9.2011

there's nothing from 0 to pi, and from -3pi to -4pi since i need where sin is negative?

Thanks for the help!

 

[Quaid]

If sin(theta)= -.1234, find all (theta) in [-4pi,pi] that make this eq true?

what i have so far:

sin is negative in QIII,QIV

sin^-1(-.1234)=-.1237

0 - .1237 = -.1237

-pi + .1237 = -3.0179

-2pi - .1237 = -6.4069

-3pi + .1237 = -9.2011

there's nothing from 0 to pi, and from -3pi to -4pi since i need where sin is negative?

Hello Mauro:

Is the digit 2 highlighted in red a typo? (I got -9.3011, rounded.)

The interval phrase (also in red) is backwards; -4 is a smaller value than -3, so write "from -4pi to -3pi"

The rest of your results look good!

Now use the same periodicity, to determine the four positive solutions.

Cheers

 

[mauro125]

Hello Mauro:

Is the digit 2 highlighted in red a typo? (I got -9.3011, rounded.)

The interval phrase (also in red) is backwards; -4 is a smaller value than -3, so write "from -4pi to -3pi"

The rest of your results look good!

Now use the same periodicity, to determine the four positive solutions.

Cheers

yes a typo on my part, i also got -9.3011.
since I'm going CW to get negtive values isn't -3pi before -4pi? Also since my problem is only asking for values from [-4pi,pi] and from zero to pi falls on QI, II those values are not being asked for? i'm no expert tho so correct me if im wrong and thank you very much for your time and input

 

[Quaid]

since I'm going CW to get negtive values isn't -3pi before -4pi?

Okay. But, you could also have started at -4Pi and gone counter-clockwise to reach -3Pi. Then you would have written "from -4Pi to -3Pi", yes?

When we express intervals on the Real number line, there is a standard to avoid ambiguity. The standard is to go from left to right.

(This is why the exercise does not state [Pi, -4Pi], either.)

my problem is only asking for values from [-4pi,pi] …

Right you are, by Jove! (My tired 'ol peepers saw '4' where there is none.)

 

[mauro125]

Okay. But, you could also have started at -4Pi and gone counter-clockwise to reach -3Pi. Then you would have written "from -4Pi to -3Pi", yes?

When we express intervals on the Real number line, there is a standard to avoid ambiguity. The standard is to go from left to right.

(This is why the exercise does not state [Pi, -4Pi], either.)

forgive me I didn't want to seem like I know what I'm talking about I just started trig so thank you for clarifying. also, I don't need values from from -4pi to -3pi right 'cause they would fall on where sin(QI,QII) is positive?