Math Is Fun Forum

lolol

Member

Registered: 2008-07-25

Posts: 1

If a trig equation has one answer, how many answers will it have?

If a trig equation has one answer, how many answers will it have? (Provided you do not restrict the domain?)

Unsure about this. Any help would be appreciated, thanks.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: If a trig equation has one answer, how many answers will it have?

If a trig equation has one answer, how many answers will it have?

This is like asking: If a dog has four legs, how many legs does it have?

Can you rephrase your question?

careless25

Real Member

Registered: 2008-07-24

Posts: 560

Re: If a trig equation has one answer, how many answers will it have?

If a trig equation has one answer, how many answers will it have?

This is like asking: If a dog has four legs, how many legs does it have?

Can you rephrase your question?

:

Last edited by careless25 (2008-07-25 13:38:27)

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: If a trig equation has one answer, how many answers will it have?

Let me take a guess:
Par example,
  inverse tangent of 1 is 45 degrees, but is also 45 + 180n, where n = {...-9,-8,-7...+7,+8,+9...}
So if you are standing and facing north-east, no matter how many times you turn around, you will face north-east or south-west, which are similar to a slope of 1,
or 45 degrees, if east is the x-axis, and north is the y-axis.
South-west has the same slope because -1/-1 = +1.
No one seems to care which way the line is going for
regular lines, they go in 2 directions, so
45 degrees points north-east and
135 degrees doesn't, that's perpendicular or north-west.
But add 90 more from 135, and 225 will point south-west, which
has the slope of 1.
The tangent function gives you the slope because it
divides the 2 legs of a right triangle, similarly slope
divides the vertical and horizontal "shadows" or "components"
of a diagonal line (or the hypotenuse of the right triangle just mentioned).

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igloo myrtilles fourmis

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: If a trig equation has one answer, how many answers will it have?

I'm guessing he means,
if sin(x) = a,
how many angles can satisfy the equation?

in which case the 'answers', or better, the set of values that satisfy this equation are ... an infinite number of values!

However, if you consider them as angles, and consider angles that differ by integer multiples of 360 degrees to be equivalent, then you fill find that for any angle A, you can find another B such that sin(A) = sin(B), in other words, there are two answers. The same holds for cosines.

remember its best to think of sine and cosine functions with the unit circle. The sine of an angle θ is the y coordinate you obtain from rotating the point (1,0) about the origin (counter clockwise) by θ degrees. (or radians). The cosine of θ is the x coordinate of that same point.

So you know if two angles have the same sine if they have the same vertical height on the unit circle, and the same cosine if they have the same horizontal position on the unit circle. See diagram.

But I'm only guessing at what you meant! >.< I just felt like babbling about the unit circle, because I love the unit circle! Seems to me that if you understand the unit circle, you understand trigonometry!

Last edited by mikau (2008-07-25 21:06:41)

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A logarithm is just a misspelled algorithm.