1. Trigonometry im lost

I need help with trigonometry questions please i know the answers but don't know the process to get the answers

" solve 2 cos (5x+10)=1 for 0<x<360" ans = 10 and 58

and also to solve 4 sin 2A= -3, for 0 ≤ A ≤ 2 Pi Answer = 76.72 and 166.72

please if you could show me the process it would be much appreciated as i have being trying for a few days now and am getting no where

2. Re: Trigonometry im lost

Originally Posted by derm
I need help with trigonometry questions please i know the answers but don't know the process to get the answers

" solve 2 cos (5x+10)=1 for 0<x<360" ans = 10 and 58

and also to solve 4 sin 2A= -3, for 0 ≤ A ≤ 2 Pi Answer = 76.72 and 166.72

please if you could show me the process it would be much appreciated as i have being trying for a few days now and am getting no where
$2 \cos(5x+10)=1$

$\cos(5x+10)=\frac{1}{2}$

$5x+10=\arccos\left(\frac{1}{2}\right)$

for $0 \leq x < 360$ there are two values of $\arccos\left(\frac{1}{2}\right)$, $x=60$ and $x=300$ degrees

$5x+10=60$

$5x=50$

$x=10$

$5x+10=300$

$5x=290$

$x = 58$

The second problem is similar, just be careful taking the arcsin.

3. Re: Trigonometry im lost

Cos(5x+10)=1/2 =cos60 then get the general formula for solving trig equations for cosine....to find the roots show us some of your work.....

4. Re: Trigonometry im lost

Originally Posted by derm
solve 4 sin 2A= -3, for 0 ≤ A ≤ 2 Pi Answer = 76.72 and 166.72

please if you could show me the process it would be much appreciated as i have being trying for a few days now and am getting no where
Where did you get those answers for the second problem? Did you write the problem down correctly?

It appears that A is supposed to be given in non-negative radians < $2 \pi.$ Clearly 76.72 and 166.72 are not less than $2 \pi < 6.4.$

Furthermore, these answers are clearly not correct even in degrees:

$4sin(2A) = -\ 3 \implies sin(2A) = -\ \dfrac{3}{4} = -\ 0.75.$ With me to here?

But $sin(76.72^o * 2) = sin(153.44^o) \approx 0.447 \ne -\ 0.75.$

And $sin(166.72^o * 2) = sin(333.44^o) \approx -\ 0.447 \ne -\ 0.75.$

5. Re: Trigonometry im lost

Sorry this is the correct equation that i want to solve

4 sin 2A= -3, for 0 ≤ A ≤ 2 Pi radians Answer = 1.99 and 2.72

iv changed the mode in my calculator over and back from deg to rad but i still can figure out how to get the answer !!

6. Re: Trigonometry im lost

Thanks a lot for the first answer it starting to make sense now iv tried working out the second one but a getting stuck

4 sin 2A= -3, for 0 ≤ A ≤ 2 Pi radians Answer = 1.99 and 2.72

iv changed the mode in my calculator over and back from deg to rad but i still can figure out how to get the answer !!

7. Re: Trigonometry im lost

Originally Posted by derm
Sorry this is the correct equation that i want to solve

4 sin 2A= -3, for 0 ≤ A ≤ 2 Pi radians Answer = 1.99 and 2.72

iv changed the mode in my calculator over and back from deg to rad but i still can figure out how to get the answer !!
OK. I am going to have YOU do this step by step.

Romsek has already shown you the first step

$4sin(2A) = 4 * sin(2A) = - 3 \implies sin(2A) = -\ 0.75.$ No problem up to here is there?

$sin(x) = y\ and\ -\ \dfrac{\pi}{2} \le x \le \dfrac{\pi}{2} \implies y = arcsin(x)\ and\ -\ 1 \le y \le 1.$ Are you clear on the role of the arcsin, arccos, and arctan?

So to find 2A we need to take the arcsine of what? What do you get as an answer when you set the calculator to radians?

8. Re: Trigonometry im lost

Getting -.75 if grand
No i not fully clear on the role of arcsin, arccos, and arctan

to find 2A i take the arcsin of -.75 and i get -48.59 do i convert this to rads ?

9. Re: Trigonometry im lost

Originally Posted by derm
Getting -.75 if grand
No i not fully clear on the role of arcsin, arccos, and arctan

to find 2A i take the arcsin of -.75 and i get -48.59 do i convert this to rads ?
Look at this calculation.

10. Re: Trigonometry im lost

Ok - 848062 i can do that now .

then i divide pi by 2 and i get 1.57 and 1.57? where do i go from here?

11. Re: Trigonometry im lost

Originally Posted by derm
Ok - 848062 i can do that now .

then i divide pi by 2 and 1.57 and 1.57?
Look at this

Note that $2A=-0.848062$.

12. Re: Trigonometry im lost

Originally Posted by derm
Getting -.75 if grand
No i not fully clear on the role of arcsin, arccos, and arctan

They are inverse functions (defined over a limited domain because the trigonometric functions are cyclical).

So $sin(x) = y \iff x = arcsin(y)\ if\ -\ \dfrac{\pi}{2} \le x \le \dfrac{\pi}{2}.$

to find 2A i take the arcsin of -.75 and i get -48.59 do i convert this to rads ? You can do it that way, but your calculator will do it for you if you ask for the answer in radians by setting the calculator to radians in the first place.
.

If you set the calculator to compute in degrees (the hard way):

$2A = arcsin(-\ 0.75) \approx -\ 48.59^o = -\ 48.59^o * \dfrac{2\pi\ rad}{360^o} \approx -\ 0.848\ radians.$

If you set the calculator to compute in radians (the easy way):

$2A = arcsin(-\ 0.75) \approx -\ 0.848\ radians.$

Why convert? Every conversion represents an opportunity for error (at least it does for me). Use the calculator that God gave you.

Uh oh. The answer calls for a NON-NEGATIVE answer. How do you calculate the corresponding non-negative measure from a negative measure of an angle?

13. Re: Trigonometry im lost

so do i subtract and add on -.848062 from 3.14 rads ?

14. Re: Trigonometry im lost

Originally Posted by JeffM
.

If you set the calculator to compute in degrees (the hard way):

$2A = arcsin(-\ 0.75) \approx -\ 48.59^o = -\ 48.59^o * \dfrac{2\pi\ rad}{360^o} \approx -\ 0.848\ radians.$

If you set the calculator to compute in radians (the easy way):

$2A = arcsin(-\ 0.75) \approx -\ 0.848\ radians.$

Why convert? Every conversion represents an opportunity for error (at least it does for me). Use the calculator that God gave you.

Uh oh. The answer calls for a NON-NEGATIVE answer. How do you calculate the corresponding non-negative measure from a negative measure of an angle?
Not sure but do i add them on the to the negative measures of the angle so if the angle was - .84 rads and i add on .2 rads the angle would then be -.64 rads?

15. Re: Trigonometry im lost

Originally Posted by derm
Not sure but do i add them on the to the negative measures of the angle so if the angle was - .84 rads and i add on .2 rads the angle would then be -.64 rads?
Done here.

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