1. ## Approximate values

Find the approximate values of theta between 0 degrees and 360 degrees that make the following equation a true statement:
cos thetha = -0.36467

a) Round final answer to the nearest minute
b) Round final answer to the nearest 10 minute

2. Originally Posted by subzero06
Find the approximate values of theta between 0 degrees and 360 degrees that make the following equation a true statement:
cos thetha = -0.36467

a) Round final answer to the nearest minute
b) Round final answer to the nearest 10 minute

Okay, $\displaystyle cos \theta = -0,36467$

Let's see where cos is negative.
That would be the second and third quadrants.

Now let's calculate a reference angle.

$\displaystyle x = cos ^{-1} (0,36467)$ Why did I drop the negative? Because we just determined where it will be negative. All we want now is a reference angle, which we will call $\displaystyle x$.

$\displaystyle x = 68,61272464$

Now substitute $\displaystyle x$ into the second and third quadrants.

$\displaystyle \theta = 180 - x = 111,3872$

$\displaystyle \theta = 180 + x = 248,6127$

I'm sure you can handle the rounding

3. Originally Posted by janvdl
Okay, $\displaystyle cos \theta = -0,36467$

Let's see where cos is negative.
That would be the second and third quadrants.

Now let's calculate a reference angle.

$\displaystyle x = cos ^{-1} (0,36467)$ Why did I drop the negative? Because we just determined where it will be negative. All we want now is a reference angle, which we will call $\displaystyle x$.

$\displaystyle x = 68,61272464$

Now substitute $\displaystyle x$ into the second and third quadrants.

$\displaystyle \theta = 180 - x = 111,3872$

$\displaystyle \theta = 180 + x = 248,6127$

I'm sure you can handle the rounding
111 degree 23' 14.191''
and
248 degree 36' 45.809''

correct?

4. Originally Posted by subzero06
111 degree 23' 14.191''
and
248 degree 36' 45.809''

correct?
From my calculator:

$\displaystyle 111,3872 = 111 ^{o} 23' 13.92''$ (Close enough I guess)

$\displaystyle 248.6127 = 248 ^{o} 36' 45.72''$ (Once again, close enough)

5. Originally Posted by janvdl
From my calculator:

$\displaystyle 111,3872 = 111 ^{o} 23' 13.92''$ (Close enough I guess)

$\displaystyle 248.6127 = 248 ^{o} 36' 45.72''$ (Once again, close enough)
yeah,
so

a) Round final answer to the nearest minute
ans: 111 degree 23'
ans: 248 degree 36'

b) b) Round final answer to the nearest 10 minute

ans: 111 degree 20'
ans: 248 degree 30'

6. Originally Posted by subzero06
yeah,
so

a) Round final answer to the nearest minute
ans: 111 degree 23'
ans: 248 degree 36'

b) b) Round final answer to the nearest 10 minute

ans: 111 degree 20'
ans: 248 degree 30'
Think it would be:

b) b) Round final answer to the nearest 10 minute

ans: 111 degree 20'
ans: 248 degree 40'

7. Originally Posted by subzero06
yeah,
so

a) Round final answer to the nearest minute
ans: 111 degree 23'
ans: 248 degree 36'

b) b) Round final answer to the nearest 10 minute

ans: 111 degree 20'
ans: 248 degree 30'
36 is nearer to 40 than 30

8. Originally Posted by Moo
36 is nearer to 40 than 30
oh yeah correct! lol

bcus it higher than 5