# Trigonometric Equations...1

Discussion in 'Geometry and Trigonometry' started by nycmathguy, Mar 9, 2022.

1. ### nycmathguy

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Before continuing on in the polar world, I want to post four trigonometric equations that I recently found online. I don't understand the steps to solve such equations. The following trigonometric equations are not your typical trigonometric equations. When you have time, please provide a step by step solution to each problem. Thank you so much.

Solve for x.

sin x + cos x = 0

nycmathguy, Mar 9, 2022
2. ### MathLover1

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sin x + cos x = 0
sqrt(2) sin(x + π/4) = 0

x = 1/4 (4 π n - π), n element Z

MathLover1, Mar 10, 2022
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3. ### nycmathguy

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Sorry but I don't understand what you did here? Is there an algebraic way to solve the given equation for x?

nycmathguy, Mar 10, 2022
4. ### MathLover1

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this way:
sin(x) + cos (x) =0........divide by cos (x)

sin(x)/ cos (x) + cos (x)/cos (x) =0

tan (x) + 1 =0

tan (x) =-1

x=tan^-1 (-1)

x=-π/4

general solution:

x= 3pi/4+pi* n

MathLover1, Mar 10, 2022
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5. ### nycmathguy

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You divided both sides by cos x. Could we also divide both sides by sin x, if needed?

nycmathguy, Mar 10, 2022
6. ### MathLover1

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yes, you can also divide both sides by sin x and got cot x

MathLover1, Mar 10, 2022
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7. ### nycmathguy

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Thank you.

nycmathguy, Mar 11, 2022
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