Trig Question

[ksd31]

Given the function value and the quadrant restriction, find B.

Functional Value - cosB=-.9388
Interval - (180 degrees - 270 degrees)

I am stumped on this problem, the only thing that I have determined is that B falls in quadrant III. Thanks.

 

[Deleted member 4993]

Given the function value and the quadrant restriction, find B.

Functional Value - cosB=-.9388
Interval - (180 degrees - 270 degrees)

I am stumped on this problem, the only thing that I have determined is that B falls in quadrant III. Thanks.

Are you allowed to use calculator?

 

[ksd31]

Yes, I am allowed to use a calculator.

 

[Deleted member 4993]

Yes, I am allowed to use a calculator.

So use it and find the value of B when cos(B) = -.9388 (the answer will come in 2nd, quadrant)

Then find the corresponding angle in 3 rd quadrant - remembering

\(\displaystyle \cos(\pi - \theta) \, = \, \cos(\pi + \theta)\)

 

[ksd31]

I still cannot seem to get the same answer as in the back of the book. I am obviously doing something incorrectly. I find the Cos-1(-.9388) and find 159.85. Is this correct so far?

 

[Loren]

That's what I get. Is the answer in the book in terms of degrees and minutes versus degrees and hundredths?

 

[ksd31]

The answer in the back of the book is 200.1 degrees. I still have to change my answer so that it is in the range of the third quadrant. I am still unsure as to how to do that.

 

[mmm4444bot]

The answer in the back of the book is 200.1 degrees …

Subtracting 159.85 degrees from 180 degrees gives us the reference angle 20.149 degrees.

Adding the reference angle to 180 degrees gives us the angle in Quadrant III: 200.149 degrees.

 

[ksd31]

Thank you! It makes complete sense now.

 

[mmm4444bot]

Good.

Note that I edited my post to remove the remark about improper rounding.

It's best, when using a scientific calculator, to not round-off intermediate results. Since the calculator retains previous results in memory, just carry all of the digits until the very last calculation. Then round once, at the very end.

Otherwise, we'd get 200.2 degrees.