1. ## Trig problems

Hi

I need help on the following two questions:

1) An angle is measured at 2.1 radians.
a) What is its measure in degrees, minutes and seconds ( to the nearest second)?
b) What is its sine?

This is what i have done:

To convert radians to degrees you multiply by $\displaystyle \frac{180}{\pi}$

so get 120 degrees.

to get minutes i multiplied by 60 and to get seconds i multiplied by 3600

therefore it is: 7200mins, 432000seconds

How would i find the sine??

2) Write down 4 values of x (exactly, in radians) for which $\displaystyle sinx = \frac{-1}{2}$ and circle the value which equals $\displaystyle arcsin(\frac{-1}{2})$?

This is what i have done:
So firstly i wrote down when sin is -0.5, which is in the 3rd and 4th quadrant.

i know that $\displaystyle sinx = -0.5 = \frac{\pi}{6}$

so...

$\displaystyle \pi + \frac{\pi}{6}, 2\pi - \frac{\pi}{6}, 2\pi + \frac{\pi}{6}, 3\pi - \frac{\pi}{6}$

final values are: $\displaystyle \frac{7\pi}{6}, \frac{11\pi}{6}, \frac{13\pi}{6}, \frac{17\pi}{6}$

Not sure if this is correct.

P.S

2. 1a) For the first problem what you did was to first find an approximation of the anwer in degrees and then you convereted that approximation to minutes, and then to seconds. But what I think they want is a more exact conversion expresed in degrees, minutes, and seconds:
$\displaystyle 2.1 \ rad \times \frac {180 ^{\small o}} {\pi \ rad} = 120.3211^{\small o}$

So it's 120 degrees PLUS a bit more, and you need now to convert the remainder to minutes, then seconds:
$\displaystyle 0.3211^{ \small o} \times \frac {60 \ min} {deg} = 19.628 '.$
Now convert this remainder of this to seconds:
$\displaystyle 0.628 \ min \times \frac {60"} {min} = 16.1",$ which rounds to 16".
So you have: $\displaystyle 2.1 \ rad = 120^{\small o}\ 19'\ 16"$.

1b) To find the sine you can use a calculator, but it's very close to $\displaystyle \sin \frac {2 \pi} {3} = \frac {\sqrt {3}} {2}$.

2) Your answers of $\displaystyle \frac 7 6 \pi$ and $\displaystyle \frac{11} {6} \pi$ are good, but the other two answer are in the wrong quadrants - they have sine of +1/2. You can either add or subtract a multiple of 2 $\displaystyle \pi$ to your first two answers.

3. ok thanks, but why would i use the remainder instead of the 120 degrees to find the minutes?

4. Originally Posted by Paymemoney
ok thanks, but why would i use the remainder instead of the 120 degrees to find the minutes?
Angles are measured in degrees, minutes, and seconds. This is similar to how we measure time - in hours, minutes and seconds. Suppose I asked you to convert 0.12 days into hours, minutes, and seconds - you would proceed like this:

$\displaystyle 0.12 \ Days \times \frac {24 \ hr} {Day}\ = \ 2.88 \ Hr = 2 \ Hr \ + \ 0.88 \ Hr$

$\displaystyle 0.88 \ Hr \times \frac {60 \ Min} {Hr} = 52.8 \ Min = 52\ Min \ + \ 0.8 \ Min$

$\displaystyle 0.8 \ Min \times \frac { 60 \ Sec} {Min} = 48 \ Sec$

Thus 0.12 Days = 2 Hr, 52 Min, 48 Sec.

See how it works?