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\sin \theta=\frac{5}{13}, find the remaining trigonometric ratios.13 |
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Answer» sinθ= 5/13 [Given] ∴cosecθ= 1/sinθ= 1÷ (5/13) ∴cosecθ= 13/5 We know that, sin2θ+ cos2θ= 1 ∴(5/13)2+ cos2θ= 1 ∴25/169 + cos2θ= 1 ∴cos2θ= 1 – 25/169 ∴cos2θ= (169 – 25 )/169 ∴cos2θ= 144/169 ∴cosθ= ±√ (144/169) ∴cosθ= ±12/13 But,θis an acute angle [Given] ∴All trigonometric ratios must be positive, ∴cosθ= 12/13 secθ= 1/cosθ ∴secθ= 1÷ (12/13) ∴secθ= 13/12 tanθ= sinθ÷ cosθ ∴tanθ= 5/13 ÷ 12/13 ∴tanθ= 5/13 × 13/12. ∴tanθ= 5/12 cotθ= 1/tanθ ∴cotθ= 1÷ (5/12) ∴cotθ= 12/5 |
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