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trigonometry a-level maths question... HELP!
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If someone can go through this question and tell me the answer that would be great! (or how to get to the answer)
f(x) = 2 cos^-1(x) -1
1. Find the range and domain
2. find the exact value of f(-0.5)
3. Find f^-1(x)
f(x) = 2 cos^-1(x) -1
1. Find the range and domain
2. find the exact value of f(-0.5)
3. Find f^-1(x)
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#2
(Original post by grapefruits)
If someone can go through this question and tell me the answer that would be great! (or how to get to the answer)
f(x) = 2 cos^-1(x) -1
1. Find the range and domain
2. find the exact value of f(-0.5)
3. Find f^-1(x)
If someone can go through this question and tell me the answer that would be great! (or how to get to the answer)
f(x) = 2 cos^-1(x) -1
1. Find the range and domain
2. find the exact value of f(-0.5)
3. Find f^-1(x)
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#3
ok so the domain is -1 to 1 because thats the domain of arccos (cos^-1) ye. the range is -1 to 2pi-1 , because the range of arccos is 0 to pi (so double that and subtract one).
f(-0.5) = 2 * arccos(0.5) - 1 = 2 * pi/3 - 1 = 2pi/3 - 1 ~= 1.094
get f^-1(x) as follows:
y=f(x)=2arccos(x)-1
y+1=2arccos(x)
(y+1)/2=arccos(x)
cos((y+1)/2)=x
f^-1(x)=cos((x+1)/2)
f(-0.5) = 2 * arccos(0.5) - 1 = 2 * pi/3 - 1 = 2pi/3 - 1 ~= 1.094
get f^-1(x) as follows:
y=f(x)=2arccos(x)-1
y+1=2arccos(x)
(y+1)/2=arccos(x)
cos((y+1)/2)=x
f^-1(x)=cos((x+1)/2)
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#4
(Original post by jakesimian)
ok so the domain is -1 to 1 because thats the domain of arccos (cos^-1) ye. the range is -1 to 2pi-1 , because the range of arccos is 0 to pi (so double that and subtract one).
f(-0.5) = 2 * arccos(0.5) - 1 = 2 * pi/3 - 1 = 2pi/3 - 1 ~= 1.094
get f^-1(x) as follows:
y=f(x)=2arccos(x)-1
y+1=2arccos(x)
(y+1)/2=arccos(x)
cos((y+1)/2)=x
f^-1(x)=cos((x+1)/2)
ok so the domain is -1 to 1 because thats the domain of arccos (cos^-1) ye. the range is -1 to 2pi-1 , because the range of arccos is 0 to pi (so double that and subtract one).
f(-0.5) = 2 * arccos(0.5) - 1 = 2 * pi/3 - 1 = 2pi/3 - 1 ~= 1.094
get f^-1(x) as follows:
y=f(x)=2arccos(x)-1
y+1=2arccos(x)
(y+1)/2=arccos(x)
cos((y+1)/2)=x
f^-1(x)=cos((x+1)/2)
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#5
(Original post by old_engineer)
All looks good. Just one point: you should leave the answer to Q2 in exact form.
All looks good. Just one point: you should leave the answer to Q2 in exact form.
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Thank you so much @old_engineer and @username4261208. It all makes sense and I was able to then solve similar problems.
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