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in Trigonometry by (47.6k points)
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If sin θ = 7/25 , find the values of cos θ and tan θ.

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in sin θ = 7/25  … [Given] 

We know that, 

sin2 θ + cos2 θ = 1

…[Taking square root of both sides] 

Now, tanθ = sin\(\theta\)/cosθ

Alternate Method: 

sin θ = 7/25 …(i) [Given] 

Consider ∆ABC, where ∠ABC 90° and ∠ACB = θ. 

sin θ = AB/AC … (ii) [By definition] 

∴ AB/AC = 7/25 … [From (i) and (ii)]

LetAB = 7k and AC = 25k 

In ∆ABC, ∠B = 90° 

∴ AB2 + BC2 = AC2 … [Pythagoras theorem] 

∴ (7k)2 + BC2 = (25k)2

∴ 49k2 + BC2 = 625k2 

∴ BC2 = 625k2 – 49k2

∴ BC2 = 576k2 

∴ BC = 24k …[Taking square root of both sides]

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