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Show that $2θ + 2sinθ - 1 = pi/3.$
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)Apply trigonometric relationships in solving problems?Radius of circle by knowing a cross section.A few questions regarding the cosine difference identityFinding angles in spherical triangle using law of cosinesLength of all sides of a triangle, knowing one angle one length and the perimeter of the triangle.How do you prove that in a circle the angle subtended at the cente is proportional to its arc length using symmetry?How to interpret making “angles of $mathbf 30^circ$ and $mathbf60^circ $ with the horizontal line parallel to the ground”?Trigonometry of an hyperbolic Omega TriangleTrigonometry dealing with rubber bands around touching discsCircles Problem Solving Question
$begingroup$
Need help with this question:
The diagram shows that the cross section ABCD of a glass prism. AD = BC = 4cm and both are at right angles to DC. AB is the arc of a circle, centre O and radius 6cm. Given that angle AOB = 2 radians and that the perimeter of the cross-section is 2(7 + pi), show that (2θ + 2sinθ - 1) = pi/3.
Here is a (bad) diagram of the thing:
What I did so far: I worked out AB arc length = 12θ and I was going to use the cosine rule to work out the direct straight length of AB to find out what CD was, but I don't see how the sin comes into play.
trigonometry
edited Oct 24 '12 at 18:56
Emily
29.6k469112
asked Oct 24 '12 at 17:56
Wk_of_AngmarWk_of_Angmar
182110
$endgroup$
add a comment |
$begingroup$
Need help with this question:
The diagram shows that the cross section ABCD of a glass prism. AD = BC = 4cm and both are at right angles to DC. AB is the arc of a circle, centre O and radius 6cm. Given that angle AOB = 2 radians and that the perimeter of the cross-section is 2(7 + pi), show that (2θ + 2sinθ - 1) = pi/3.
Here is a (bad) diagram of the thing:
What I did so far: I worked out AB arc length = 12θ and I was going to use the cosine rule to work out the direct straight length of AB to find out what CD was, but I don't see how the sin comes into play.
trigonometry
edited Oct 24 '12 at 18:56
Emily
29.6k469112
asked Oct 24 '12 at 17:56
Wk_of_AngmarWk_of_Angmar
182110
$endgroup$
$begingroup$
Hint: Why does the result involve $sin theta$ instead of $sin (2theta)$?
$endgroup$
– hwhm
Oct 24 '12 at 19:00
add a comment |
$begingroup$
Need help with this question:
The diagram shows that the cross section ABCD of a glass prism. AD = BC = 4cm and both are at right angles to DC. AB is the arc of a circle, centre O and radius 6cm. Given that angle AOB = 2 radians and that the perimeter of the cross-section is 2(7 + pi), show that (2θ + 2sinθ - 1) = pi/3.
Here is a (bad) diagram of the thing:
What I did so far: I worked out AB arc length = 12θ and I was going to use the cosine rule to work out the direct straight length of AB to find out what CD was, but I don't see how the sin comes into play.
trigonometry
edited Oct 24 '12 at 18:56
Emily
29.6k469112
asked Oct 24 '12 at 17:56
Wk_of_AngmarWk_of_Angmar
182110
$endgroup$
Need help with this question:
The diagram shows that the cross section ABCD of a glass prism. AD = BC = 4cm and both are at right angles to DC. AB is the arc of a circle, centre O and radius 6cm. Given that angle AOB = 2 radians and that the perimeter of the cross-section is 2(7 + pi), show that (2θ + 2sinθ - 1) = pi/3.
Here is a (bad) diagram of the thing:
What I did so far: I worked out AB arc length = 12θ and I was going to use the cosine rule to work out the direct straight length of AB to find out what CD was, but I don't see how the sin comes into play.
trigonometry
trigonometry
edited Oct 24 '12 at 18:56
Emily
29.6k469112
asked Oct 24 '12 at 17:56
Wk_of_AngmarWk_of_Angmar
182110
edited Oct 24 '12 at 18:56
Emily
29.6k469112
asked Oct 24 '12 at 17:56
Wk_of_AngmarWk_of_Angmar
182110
edited Oct 24 '12 at 18:56
Emily
29.6k469112
edited Oct 24 '12 at 18:56
Emily
29.6k469112
edited Oct 24 '12 at 18:56
Emily
29.6k469112
29.6k469112
asked Oct 24 '12 at 17:56
Wk_of_AngmarWk_of_Angmar
182110
asked Oct 24 '12 at 17:56
Wk_of_AngmarWk_of_Angmar
182110
asked Oct 24 '12 at 17:56
Wk_of_AngmarWk_of_Angmar
182110
182110
$begingroup$
Hint: Why does the result involve $sin theta$ instead of $sin (2theta)$?
$endgroup$
– hwhm
Oct 24 '12 at 19:00
add a comment |
$begingroup$
Hint: Why does the result involve $sin theta$ instead of $sin (2theta)$?
$endgroup$
– hwhm
Oct 24 '12 at 19:00
$begingroup$
Hint: Why does the result involve $sin theta$ instead of $sin (2theta)$?
$endgroup$
– hwhm
Oct 24 '12 at 19:00
$begingroup$
Hint: Why does the result involve $sin theta$ instead of $sin (2theta)$?
$endgroup$
– hwhm
Oct 24 '12 at 19:00
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Hint: $fracDC2 = 6sintheta$.
answered Oct 24 '12 at 19:03
Hagen von EitzenHagen von Eitzen
283k23273508
$endgroup$
add a comment |
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$begingroup$
Hint: $fracDC2 = 6sintheta$.
answered Oct 24 '12 at 19:03
Hagen von EitzenHagen von Eitzen
283k23273508
$endgroup$
add a comment |
$begingroup$
Hint: $fracDC2 = 6sintheta$.
answered Oct 24 '12 at 19:03
Hagen von EitzenHagen von Eitzen
283k23273508
$endgroup$
add a comment |
$begingroup$
Hint: $fracDC2 = 6sintheta$.
answered Oct 24 '12 at 19:03
Hagen von EitzenHagen von Eitzen
283k23273508
$endgroup$
Hint: $fracDC2 = 6sintheta$.
answered Oct 24 '12 at 19:03
Hagen von EitzenHagen von Eitzen
283k23273508
answered Oct 24 '12 at 19:03
Hagen von EitzenHagen von Eitzen
283k23273508
answered Oct 24 '12 at 19:03
Hagen von EitzenHagen von Eitzen
283k23273508
answered Oct 24 '12 at 19:03
Hagen von EitzenHagen von Eitzen
283k23273508
283k23273508
add a comment |
add a comment |
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$begingroup$
Hint: Why does the result involve $sin theta$ instead of $sin (2theta)$?
$endgroup$
– hwhm
Oct 24 '12 at 19:00