Thread: solving trig equations

can somebody please help me
I have the question and answer to this question but i do not understand at all how the answer is concluded

Q: in the range 0<=x<=2Pi solve Sin2x=-1
A:3Pi/8 and 7Pi/8

could somebody maybe briefly explain how you work this out

thanks

For angles ranging from 0 to 360,
Sin(angle) may be viewed as the y co-ordinate of a point on a unit circle,
of radius 1.

If 2x is the angle,
where is the y co-ordinate -1 ?

answer: at 270 degrees, or

Sin(270 degrees)= -1.

So 2x is 270 degrees or 270+n(360) degrees, n=0,1,2,3........

x is

The second result is obtained for 2x=270+360 degrees,
as x<360 degrees.

Hello, wahhdoe!

Solve: .

Answers: . . These are wrong! **

We are expect to know that: .


We have: .

. . Then: .

. . Hence: .


The roots in the given range are: .


~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

**

Maybe the problem was: .

Even then, their answer is wrong.
. . There are more answers in that range.


If the problem is: .

. . then we have: .


Therefore: .