Signs of Trigonometric Ratios

Things to remember

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1. If n is even, there will be no change in the trigonometric ratios.
   i.e. sin(n × 90° ± \(\theta\))⇒ sin \(\theta\)
   cos(n × 90° ± \(\theta\))⇒ cos \(\theta\), etc.
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2. If n is odd, then the trigonometric ratios change as follows:
   sin(n × 90° ± \(\theta\))⇒ cos \(\theta\)
   cos(n × 90° ± \(\theta\))⇒ sin \(\theta\)
   tan(n × 90° ± \(\theta\))⇒ cot \(\theta\)
   cosec(n × 90° ± \(\theta\))⇒sec \(\theta\)
   sec(n × 90° ± \(\theta\))⇒ cosec \(\theta\)
   cot(n × 90° ± \(\theta\))⇒ tan \(\theta\)
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3. The sign of the trigonometric ratio of the angle(n × 90° ± \(\theta\)) is determined by taking into consideration that in which quadrant that angle(n × 90° ± \(\theta\)) lies.
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