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# Trigonometric Equations watch

1. Can anyone help me solve this equation sin(2 θ+50°)=0.5
2. Moved to the Maths section
3. Is there a range for the solutions? because there're an infinite number of solutions.

Do you typically use the cast diagram or the sin graph?

What have you tried so far?
4. (Original post by cosv)
Can anyone help me solve this equation sin(2 θ+50°)=0.5

so
hence
5. (Original post by cosv)
Can anyone help me solve this equation sin(2 θ+50°)=0.5
What are the boundaries for theta e.g. 0<θ<360°
6. (Original post by mc1996)
What are the boundaries for theta e.g. 0<θ<360°
Yes, the boundaies for theta are 0 to 360
7. (Original post by cosv)
Yes, the boundaies for theta are 0 to 360
2θ+50° = 150 boundaries change to 50°<2θ+50°<770
= 390
= 510
= 750
θ = 50
θ =170
θ =230
θ =350
8. (Original post by mc1996)
x

Forum policy.
9. (Original post by mc1996)
2θ+50° = 150 boundaries change to 50°<2θ+50°<770
= 390
= 510
= 750
θ = 50
θ =170
θ =230
θ =350
Whoever is this ‘mc1996’? He has written something that is erroneous – extremely erroneous at that. A true mathematician would understand that you cannot merely pick up a solution without writing in a logical and methodical manner. One of your solutions, ‘50’ has appeared from nowhere. You are supposed to write out the full solutions of u before getting the values of theta. Let u =2θ+50. u =150, 390, 510, 750. Therefore x =50, 155, 230, 350. What you have written here strongly suggests that you lack the required knowledge to study even GCSE Mathematics, let alone AS/A2. I suggest you go back to the basics before correcting people – incorrectly.
10. (Original post by natnalie)
Whoever is this ‘mc1996’? He has written something that is erroneous – extremely erroneous at that. A true mathematician would understand that you cannot merely pick up a solution without writing in a logical and methodical manner. One of your solutions, ‘50’ has appeared from nowhere. You are supposed to write out the full solutions of u before getting the values of theta. Let u =2θ+50. u =150, 390, 510, 750. Therefore x =50, 155, 230, 350. What you have written here strongly suggests that you lack the required knowledge to study even GCSE Mathematics, let alone AS/A2. I suggest you go back to the basics before correcting people – incorrectly.
the harshness is strong in this one
11. (Original post by mc1996)
2θ+50° = 150 boundaries change to 50°<2θ+50°<770
= 390
= 510
= 750
θ = 50
θ =170
θ =230
θ =350
Can you please explain how you reached this answer? I get similar numbers for θ but I think I am missing a step.
12. (Original post by cosv)
Can you please explain how you reached this answer? I get similar numbers for θ but I think I am missing a step.
So the original questions was Sin(2θ+50)=0.5
next we do acrsin(0.5) to find 2θ+50. arcsin(0.5)=30
2θ+50 = 30 however the boundaries have changed to 50<2θ+50<770
30 does not appear within these boundaries. This means that we cannot use 30 to find a value of θ
However from the unit circle or sine graph, sin30 is the same as sin150, sin390, sin510 and sin750. All these values appear within our boundaries
Hence, 2θ+50 = 150, 390, 510, 750
making each one equal to 2θ+50, we can find a value of θ
13. (Original post by mc1996)
...

Please do not give full solutions and it is against the forum policy
14. (Original post by TenOfThem)

Please do not give full solutions and it is against the forum policy
my apologies
15. (Original post by mc1996)
my apologies
'mc1996' since you seem like a person who is quite confident on their mathematical ability, would you please help me with this question.

The curve C has equation xy = 1/2. The tangents to C at the distinct points P(p, 1/2p)
and Q(q, 1/2q), where p and q are positive, intersect at T and the normals to C at these points intersect at N. Show that T is the point ((2pq)/(p + q),1/(p + q)).
In the case pq = 1/2 , find the coordinates of N. Show (in this case) that T and N lie on the
line y = x and are such that the product of their distances from the origin is constant.

I understand how to attempt the first part but I'm finding it hard to complete the question. Any help on this question is appreciated as long as it isn't erroneous in any way!
16. (Original post by natnalie)
Whoever is this ‘mc1996’? He has written something that is erroneous – extremely erroneous at that. A true mathematician would understand that you cannot merely pick up a solution without writing in a logical and methodical manner. One of your solutions, ‘50’ has appeared from nowhere. You are supposed to write out the full solutions of u before getting the values of theta. Let u =2θ+50. u =150, 390, 510, 750. Therefore x =50, 155, 230, 350. What you have written here strongly suggests that you lack the required knowledge to study even GCSE Mathematics, let alone AS/A2. I suggest you go back to the basics before correcting people – incorrectly.

(Original post by natnalie)
'mc1996' since you seem like a person who is quite confident on their mathematical ability, would you please help me with this question.

The curve C has equation xy = 1/2. The tangents to C at the distinct points P(p, 1/2p)
and Q(q, 1/2q), where p and q are positive, intersect at T and the normals to C at these points intersect at N. Show that T is the point ((2pq)/p + q,1/(p + q)).
In the case pq = 1/2 , find the coordinates of N. Show (in this case) that T and N lie on the
line y = x and are such that the product of their distances from the origin is constant.

I understand how to attempt the first part but I'm finding it hard to complete the question. Any help on this question is appreciated as long as it isn't erroneous in any way!
Hmmmmmmm quite a change of heart here
17. (Original post by TenOfThem)
Hmmmmmmm quite a change of heart here
Necessity makes strange bedfellows, even on TSR
18. (Original post by davros)
Necessity makes strange bedfellows, even on TSR
True

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