Final answer to the problem
$z=2\pi n+\frac{-1}{4}\pi,\:z=\frac{-1}{4}\pi\:,\:\:n\in\Z$
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Step-by-step Solution
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- Express in terms of sine and cosine
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1
Apply the addition formula: $\sin\left(x+\frac{\pi}{4}\right)=\frac{\sin\left(x\right)}{\sqrt{2}}+\frac{\cos\left(x\right)}{\sqrt{2}}$
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$\sqrt{2}\sin\left(z+45\right)=0$
Learn how to solve trigonometric equations problems step by step online. Solve the trigonometric equation cos(z)+sin(z)=0. Apply the addition formula: \sin\left(x+\frac{\pi}{4}\right)=\frac{\sin\left(x\right)}{\sqrt{2}}+\frac{\cos\left(x\right)}{\sqrt{2}}. Divide both sides of the equation by \sqrt{2}. Zero divided by anything is equal to zero. The angles where the function \sin\left(z+45\right) is 0 are.
Final answer to the problem
$z=2\pi n+\frac{-1}{4}\pi,\:z=\frac{-1}{4}\pi\:,\:\:n\in\Z$
