What is the solution for the equation sinx=cosx?

sinx = cosx

divide by cosx :

sinx/cosx = 1

From your own knowledge sinx/cosx is tanx

therefore:

Tanx = 1

Now tan is positive in the first quarter and the third quarter. To know this you use the square All Station To Central. 

The Capitals remind you when the sin , cos, tan are positive. 

This square goes anticlockwise. So in the first quarter, all are positive, second only sin, third only tan, fourth only cos. 

So tan is positive in the first and third quadrant. 

Now take inverse tan on both sides. 

this gives x = 45 degrees

Now this is for the first quadrant, to get the angle for the third quadrant you add this to 180 degrees.

Therefore the angle in the third quadrant is 180 + 45 = 225 degrees

Therefore x = 45 degrees or 225 degrees.``

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