Values of ?

[sail0r]

Having some difficulties with this concept. How do I go about doing this?

Determine all values of ?, to one decimal place, for -????3?

sin?=7/8 & tan?=-4.25 (I don't know if it will be a different approach for tan)

 

[skeeter]

I assume you're using a calculator. Note that the calculator will return a single angle value, \(\displaystyle \theta\) , in quadrant I ...
\(\displaystyle 0 < \theta < \frac{\pi}{2}\).

There is also an angle in quadrant II whose sine is 7/8. this angle is equal to \(\displaystyle \pi - \theta\)

Note that there will also be angles coterminal with the two angles above between \(\displaystyle 2\pi\) and \(\displaystyle 3\pi\) ...
\(\displaystyle \theta + 2\pi\) and \(\displaystyle (\pi - \theta) + 2\pi\)


the primary angle, \(\displaystyle \theta\), whose tangent is -4.25 is in quadrant IV ... the calculator will give you this angle.

there is also a quadrant II angle, \(\displaystyle \theta + \pi\) , whose tangent is -4.25.

finally there will be one more coterminal with the one above between \(\displaystyle \frac{5\pi}{2}\) and \(\displaystyle 3\pi\) ...

\(\displaystyle (\theta + \pi) + 2\pi\)

in summary, remember that angles with a positive sine value reside in quadrants I and II ... angles with a negative tangent value reside in quadrants II and IV.

 

[PAULK]

Having some difficulties with this concept. How do I go about doing this?

Determine all values of ?, to one decimal place, for -????3?

sin?=7/8 & tan?=-4.25 (I don't know if it will be a different approach for tan)

This does not look right. If sin ? = 7/8, then cos ? = +- sqrt(15)/8, and
tan ? = +- 7/sqrt(15). Without looking at the calculator, sqrt(15) is a little less than 4, so this is close to 2, NOT 4.25

Anyway, Quadrant II looks right and the rest of the analysis is OK, too.

 

[Deleted member 4993]

Having some difficulties with this concept. How do I go about doing this?

Determine all values of ?, to one decimal place, for -????3?

sin?=7/8 & tan?=-4.25 (I don't know if it will be a different approach for tan)

This does not look right. If sin ? = 7/8, then cos ? = +- sqrt(15)/8, and
tan ? = +- 7/sqrt(15).

I think the poster is talking about two different problems with that "and".

Without looking at the calculator, sqrt(15) is a little less than 4, so this is close to 2, NOT 4.25

Anyway, Quadrant II looks right and the rest of the analysis is OK, too.

 

[mathmarauder]

Great Job lol