-7.3.97 find x in degrees

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In summary, we are solving the equation 3sin^2x - sinx - 1 = 0 for x in degrees. We rewrite it as 3u^2 - u - 1 = 0 and use the quadratic formula to get two solutions for u. Then, we use the inverse sine function to get the values of x in degrees, which turn out to be 50.14, 129.86, 205.74, and 334.26. It may seem weird to use the quadratic formula, but it is actually an elegant method and in subjects like Physics, decimal answers are common.
  • #1

karush

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$\tiny{\textbf{7.3.a21 Radford HS}}$
find x in degrees $\quad 3\sin^2 x -\sin x-1=0$
rewrite as $3u^2-u-1=0$
quadradic eq
$u=\dfrac{1\pm \sqrt{13}}{6}$

ok this is ?? are we going to have decimal degrees?
 
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  • #2
for $0^\circ \le x < 360^\circ$

$x = \arcsin\left(\dfrac{1+\sqrt{13}}{6}\right) = 50.14^\circ \text{ and } 129.86^\circ$

$x = \arcsin\left(\dfrac{1-\sqrt{13}}{6}\right) = 205.74^\circ \text{ and } 334.26^\circ$
 
  • #3
karush said:
$\tiny{\textbf{7.3.a21 Radford HS}}$
find x in degrees $\quad 3\sin^2 x -\sin x-1=0$
rewrite as $3u^2-u-1=0$
quadradic eq
$u=\dfrac{1\pm \sqrt{13}}{6}$

ok this is ?? are we going to have decimal degrees?
Unless you just happen to know what \(\displaystyle asn \left ( \dfrac{1 \pm \sqrt{13}}{6} \right )\) is then, yes, your angle will be ugly!

-Dan
 
  • #4
i just thot having to use quadradic eq was weird
there was no answer given

Well I remember helping in surveying that the degrees were carried out 4 decimal places
or degree minutes secconds
but we never used trig... the instrument did it all for us.
 
  • #5
karush said:
i just thot having to use quadradic eq was weird
there was no answer given

Well I remember helping in surveying that the degrees were carried out 4 decimal places
or degree minutes secconds
but we never used trig... the instrument did it all for us.
I think the method with the quadratic is rather elegant. And hey, in Physics almost all of the answers are decimals!

-Dan
 
  • #6
thank God for the metric system:)
 

1. What is the value of x in degrees?

The value of x in degrees is -7.3.97.

2. How do you find x in degrees?

To find x in degrees, you can use a calculator or solve the equation -7.3.97 = x.

3. Is -7.3.97 a valid degree measurement?

No, -7.3.97 is not a valid degree measurement. Degrees should only be expressed as whole numbers or decimals, not a combination of both.

4. Can x be negative in degrees?

Yes, x can be negative in degrees. Negative degrees indicate a direction in the opposite direction of positive degrees.

5. How do you convert -7.3.97 to degrees?

To convert -7.3.97 to degrees, you can use the formula x = degrees + minutes/60 + seconds/3600. In this case, -7.3.97 degrees would be equivalent to -7 degrees, 3 minutes, and 58.2 seconds.

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