# Trig question

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#1
hi guys

today has been a real wake up call and i know for sure i need to work on bettering my maths ability, so i'm most likely going to be asking a ton of maths questions on here

i'll post the question below, every time i work it out i get cos-theta is equal to 2 and 1, therefore i get my primary solution theta = 0 for 1 and nothing for 2, therefore there's four solutions within the boundary. however, the correct answer is three solutions and i'm not sure where i've gone wrong (i wouldn't be surprised if it's something silly i've done). this is also non-calc.

thank you
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#2
this is the question
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3 years ago
#3
Try drawing cos x in that domain abd see how many values u get
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3 years ago
#4
(Original post by ashaxo99)
this is the question
That's a quadratic in cos. Solve the quadratic and see how many roots there are and if any have solutions for cos in the domain given
1
3 years ago
#5
(Original post by ashaxo99)
hi guys

today has been a real wake up call and i know for sure i need to work on bettering my maths ability, so i'm most likely going to be asking a ton of maths questions on here

i'll post the question below, every time i work it out i get cos-theta is equal to 2 and 1, therefore i get my primary solution theta = 0 for 1 and nothing for 2, therefore there's four solutions within the boundary. however, the correct answer is three solutions and i'm not sure where i've gone wrong (i wouldn't be surprised if it's something silly i've done). this is also non-calc.

thank you
Although you've not expressed it too clealy, your thinking is fine for the initial solutions. What are the four solutions that you think are valid? Listing them, may show you why you're in error.
1
#6

this is my working out, i mean, unless if i just don't know how to do trigonometry (seems plausible) and the solutions are actually supposed to be where y = 1, which is three points... i really don't know what i'm doing haha
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#7
(Original post by TeacherP)
That's a quadratic in cos. Solve the quadratic and see how many roots there are and if any have solutions for cos in the domain given
(Original post by ghostwalker)
Although you've not expressed it too clealy, your thinking is fine for the initial solutions. What are the four solutions that you think are valid? Listing them, may show you why you're in error.
thank you so much i just posted my working out, although i am quite confused myself with whether what i think are solutions are actually "solutions"
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3 years ago
#8
(Original post by ashaxo99)

this is my working out, i mean, unless if i just don't know how to do trigonometry (seems plausible) and the solutions are actually supposed to be where y = 1, which is three points... i really don't know what i'm doing haha
You have cos theta = 1 ie theta = 0 but there are other values ... look at other points on your graph.
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#9
(Original post by Muttley79)
You have cos theta = 1 ie theta = 0 but there are other values ... look at other points on your graph.
i'm not too sure what other points i'm supposed to be looking at (i'm sorry i'm terrible)
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3 years ago
#10
(Original post by ashaxo99)
i'm not too sure what other points i'm supposed to be looking at (i'm sorry i'm terrible)
Which other values of theta have y value 1 ... hint look at 2pi and ...
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#11
(Original post by Muttley79)
Which other values of theta have y value 1 ... hint look at 2pi and ...
Ooo.. so when it says cos-theta is 1, am i supposed to be looking for points where the graph touches 1.. so at 0, 2pi and 4 pi?
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3 years ago
#12
(Original post by ashaxo99)
Ooo.. so when it says cos-theta is 1, am i supposed to be looking for points where the graph touches 1.. so at 0, 2pi and 4 pi?
Yah! That's it ... well done. You keep looking until you reach the end of the range ...
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