#1
Really sorry if i can't explain this right and I have a feeling i'll get abuse for being dense, but i'm self teaching and maybe i've just missed a real simple explanation that you guys think is obvious.

I get how to change from degree to radians when pi rad = 180deg, but what I don't get is when a question is written in radians, so i can calculate the answer making sure my calculator is in correct mode, but how do i then find multiple answer?

This is a specific Question i'm stuck on,

it says solve for 0 to 2 pi inclusive, so that tell me we are in rad

solve sin x = 0.7

so my calculator works out that in rad mode answer is 0.78 correct, but then in answers there's a second answer of 2.37 how do i work this out.

i can't work out, because i know i'm not fully understanding what the answer on my calc is giving me,

if it was in degrees or even if i manually converted the degree into radians, ie sin x = 0.5 gives answer 30deg = pi/6 and i could also find the multiples givin same answer, 150deg or 5/6pi would be same answer aswel.

but i'm baffled when the question is in radians.

0
7 years ago
#2
sin x =0.7 gives a principal value of 0.78 rad.
The other solution is pi-0.78 =2.37
1
7 years ago
#3
When you find multiple solutions when working with degrees, I'm guessing you would sketch the graph or use a CAST diagram to help? When you do this, you're comparing the angle to 90, 180 etc.

When you're working in radians, you do a similar method but instead of adding/subtracting 90, 180 etc you would add/subtract pi/2, pi etc.

If your answer in radians is a multiple of pi then it's easier to compare it to pi/2, pi etc. However if it's just a decimal then you would need to compare it to 1.57, 3.14 etc. The way to get those numbers is by typing pi/2, pi etc into your calculator. With practise, you'll be able to get a feel for whether a particular angle is close to pi or zero or whatever, and hence work out where it would lie on the diagram when you calculate the other angles.
1
#4
(Original post by vc94)
sin x =0.7 gives a principal value of 0.78 rad.
The other solution is pi-0.78 =2.37
ok cool thanks,
doesn't exactly help me understand the whole subject but i don't think someone would be able to in writing.

But that at least tells me where the other answer comes from, fairly simple now you've pointed it out.

Presumably if the answer was based on cos curve you would do 2pi - 0.78??

thanks
0
7 years ago
#5
(Original post by skippy83)
ok cool thanks,
doesn't exactly help me understand the whole subject but i don't think someone would be able to in writing.

But that at least tells me where the other answer comes from, fairly simple now you've pointed it out.

Presumably if the answer was based on cos curve you would do 2pi - 0.78??

thanks
Yes, for cos you would take 2pi-0.78 or -0.78.
For sin and cos you generate more solutions by adding or subtracting multiples of 2pi.

For the tan case, you just add/subtract multiples of pi to the principal value.
0
#6
(Original post by ttoby)
When you find multiple solutions when working with degrees, I'm guessing you would sketch the graph or use a CAST diagram to help? When you do this, you're comparing the angle to 90, 180 etc.

When you're working in radians, you do a similar method but instead of adding/subtracting 90, 180 etc you would add/subtract pi/2, pi etc.

If your answer in radians is a multiple of pi then it's easier to compare it to pi/2, pi etc. However if it's just a decimal then you would need to compare it to 1.57, 3.14 etc. The way to get those numbers is by typing pi/2, pi etc into your calculator. With practise, you'll be able to get a feel for whether a particular angle is close to pi or zero or whatever, and hence work out where it would lie on the diagram when you calculate the other angles.

(Original post by vc94)
Yes, for cos you would take 2pi-0.78 or -0.78.
For sin and cos you generate more solutions by adding or subtracting multiples of 2pi.

For the tan case, you just add/subtract multiples of pi to the principal value.
thanks, that very helpful, so the decimal answers on my calculator is 0.78pi rad How would i convert this to degrees? cos when i normally change to degrees, i times by 180/pi but when i times 0.78 by this i get 140.4deg,
although when i just work out sin x =0.7 i get 44.4deg
so what simple aspect am i missing, is the 0.7 in the question, not a normal ratio is it something in respect to pi? if this makes sense.

Thanks for the help so far guys, i thought this was gonna be the end of me and i'm only at Core 2 ha. but you've made it clearer so far.
0
7 years ago
#7
(Original post by skippy83)
how do i then find multiple answer?
Use these rules:

1
7 years ago
#8
(Original post by skippy83)
thanks, that very helpful, so the decimal answers on my calculator is 0.78pi rad How would i convert this to degrees? cos when i normally change to degrees, i times by 180/pi but when i times 0.78 by this i get 140.4deg,
although when i just work out sin x =0.7 i get 44.4deg
so what simple aspect am i missing, is the 0.7 in the question, not a normal ratio is it something in respect to pi? if this makes sense.

Thanks for the help so far guys, i thought this was gonna be the end of me and i'm only at Core 2 ha. but you've made it clearer so far.
That bit in red is where you've gone wrong. Your calculator isn't saying 0.78pi radians, it's just saying 0.78 radians. Notice that sometimes an angle in radians will be given in terms of pi and sometimes it won't be.

So if you take 0.78 and times it by 180 and divide by pi then you should get the answer you're looking for.
0
#9
(Original post by Mr M)
Use these rules:

Thanks for that reference, i'll copy that onto my notes and should see me good.

(Original post by ttoby)
That bit in red is where you've gone wrong. Your calculator isn't saying 0.78pi radians, it's just saying 0.78 radians. Notice that sometimes an angle in radians will be given in terms of pi and sometimes it won't be.

So if you take 0.78 and times it by 180 and divide by pi then you should get the answer you're looking for.
:-)
Smashing lol, seriously i'm happy you've cleared that up for me, i just couldn't get my answers to be the same and I like to know the full circle to tie it all up to make sure i'm getting a full understanding of what the answer is actually telling me.

I think i understand it all now,
thanks so much to all of you, its the first issue i've had self teaching and i thought it was going to get the better of me.

Much appreciated :-)
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