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#1 2009-03-12 22:34:45
- serena
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- Registered: 2009-03-12
- Posts: 13
trignometrical identities and simple equations Q2)
2) solve the following eqns for x, giving your answers to 3 significant figures where appropriate, in the intervals indicated.
a) tan x° = 2.90, 80 ≤ x ≤ 440
&
b) cos x° = -0.809, -180 ≤ x ≤ 180
i will be very gr8full again, 
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#2 2009-03-13 00:59:21
- Jai Ganesh
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- Registered: 2005-06-28
- Posts: 48,406
Re: trignometrical identities and simple equations Q2)
a) x = 430.974°
b) x = 143.998°
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#3 2009-03-13 01:25:05
- mathsyperson
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- Registered: 2005-06-22
- Posts: 4,900
Re: trignometrical identities and simple equations Q2)
You can also get solutions by subtracting 180 from a) and taking the negative of b).
Why did the vector cross the road?
It wanted to be normal.
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#4 2009-03-16 01:19:20
- serena
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- Registered: 2009-03-12
- Posts: 13
Re: trignometrical identities and simple equations Q2)
plz explain the second technique 
i dont just want the answer, i wanna know how to GET the answer:(
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#5 2009-03-16 02:39:20
- Jai Ganesh
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- Registered: 2005-06-28
- Posts: 48,406
Re: trignometrical identities and simple equations Q2)
serena,
there are two things you must remember,
(1) the mnemonic 'All Silver Tea Cups', where A in All denoted all, that is the three trignometric ratios, sine, cos and tan, S in Silver denotes sine, T in Tea denotes tan and C in Cups denotes cos. The reason for remembering this is, in the first quadrant, where the angle is from 0° to 90°, all the angles are positive, in the second quadrant, the angle is 90° to 180°, sin is positive (implying the other ratios are negative), in the third quadrant, that is from 180° to 270°, tan is positive, and in the fourth quadrant, where the angle is from 270° to 360°, cos is positive.
(2) sin (-x) = -sin (x), cos(-x) = cos x, tan(-x) = -tan (x).
sin and tan are odd functions whereas cos is an even function.
For question (a), the answer given in post #2 was approximately 431° and the range of x given in the question was 80° to 440°. Since the periodicity of tan function is 180°, by deducting 180° from 431°, the answer, 251°, would still be correct and be within the given range.
For question (b), the answer given in post #2 was approximately 144°. since cos(-x) = cos(x), the answer -144° wold also be true and this is within the range given in the question, that is, from
-180° to 180°.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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