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Trigonometric Equations

If sinθ+cosθ=...

Question

If sin $θ + c o s θ = 0$ and $θ$ lies in 4th quadrant then find $s i n θ$ and $c o s θ$

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Solution

In 4th quadrant, cos theta is positive, but sin theta is negative.
Hence the equation can be written as $c o s θ - s i n θ = 0$ .
$\to c o s θ = s i n θ$
$\to θ = - 45 d e g$
$\to c o s θ = s i n θ = \frac{1}{(s q r o o t 2)}$ .

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