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