SOLUTION: Solve : cos X + sin X = 0 all answers in radians thanks

Question 233584: Solve : cos X + sin X = 0
all answers in radians
thanks
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
cos(x) + sin(x) = 0

They have to be equal with opposite sign so they can cancel each other out.

When x = 45 degrees, sin(x) and cos(x) are the same = .707106781

That's because they're in the first quadrant and sin(x) and cos(x) are both positive because:

opposite = length of the line is always positive.
adjacent is distance on the x-axis to the right of the y-axis and is positive.
opposite is distance on the y-axis up from the x-axis and is positive.

Go to the second quadrant and form 45 degrees up from 180 degrees.
hypotenuse is positive.
adjacent is negative (left of y-axis)
opposite is positive (up from x-axis)

the values are the same but now the sin(x) is positive and cos(x) is negative.

180 - 45 = 135 so we are talking about sin(135) and cos(135).

you get:

sin(135) + cos(135) = 0 because:

.707106781 - .707106781 = 0

Your answer is 135 degrees.

RELATED QUESTIONS
Algebraically find all solutions, in radians, to... (answered by lwsshak3)

Find the complete solution of the equation {{{cos(x)sin^2(x)-(3cos(x))/4 = 0}}} in... (answered by Edwin McCravy,solver91311)

Use algebra to find all angles theta between 0 and 2pie radians that satisfy the equation (answered by lwsshak3)

algebraically find exact values for all of the roots of the function (i.e. solve f(x)=0... (answered by venugopalramana)

How to solve for x in radians? sin^2 (x)=cos^2... (answered by solver91311)

Use inverse functions where needed to find all solutions of the equation in the interval... (answered by solver91311,stanbon)

Solve the following, finding all solutions in radians in [0,2{{{pi}}})... (answered by lwsshak3)

Hi all, I was hoping to get some help with the following problem(s) involving raidians... (answered by Alan3354)

Solve : cos(sin(x)) <... (answered by Fombitz)