Please can you tell me how to solve the following equations for values of x between (0.2 π) {π is pie}

a) tan (4x) = 1

b) sin(x-2π) + sin (x - 2π) = ½

c) 2 cos (x + ½) = -1

d) sin x + cos x = 3/2

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- March 24th 2009, 01:19 PMbigfootTrigonometric Equations Help Please!
Please can you tell me how to solve the following equations for values of x between (0.2 π) {π is pie}

a) tan (4x) = 1

b) sin(x-2π) + sin (x - 2π) = ½

c) 2 cos (x + ½) = -1

d) sin x + cos x = 3/2 - March 24th 2009, 01:41 PMgosualite
Well when you want to isolate a variable that's inside a trig function, you just take the

*inverse*trig function.

For instance, with the first problem:

.

We take of both sides (sometimes, is written and pronounced ). Get:

, so resolving the left side gives:

.

We now have to figure out what is. Well it's like asking "what angle in a right triangle gives a ratio of opposite side over adjacent side equal to 1?" It should be obvious that a 45-45-90 triangle passes this test, so resolves to , or . However, there may be more answers. Notice that works as well. In fact, for any integer*n*, , so could be any of these.

We take this info and go back to our equation:

. So:

. Then:

.

All right, but you were given a restriction of possible values, .

So we want to figure out the only values of*n*that make our solution valid. ,

,

,

.

So*n*could only be 0,1,2,3,4,5,6, or 7. - March 24th 2009, 03:44 PMbigfoot
Thanks for your help. I will try to work out the others. :)

- March 25th 2009, 02:41 AMbigfoot
How do we known that 45 degrees is pi over 4?

- March 25th 2009, 05:10 AMstapel