If sinθ = \frac{a}{b} then cos θ = ?

Foundation

Mathematics Foundation

Introduction to Trigonometry

Question

If $sinθ = \frac{a}{b}$ then cos θ = ?

$\frac{b}{a}$

$\frac{b}{\sqrt{b^{2}} - a^{2}}$

$\frac{a}{\sqrt{b^{2}} - a^{2}}$

$\frac{\sqrt{b^{2} - a^{2}}}{b}$

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Given that $\sin θ = \frac{a}{b}$ , we can use the Pythagorean identity: ${(\sin θ)}^{2} + {(\cos θ)}^{2} = 1$ . Substituting the value of sinθ gives ${(\frac{a}{b})}^{2} + {(\cos θ)}^{2} = 1$ . Solving for cosθ, we get $\cos θ = \sqrt{1 - \frac{a^{2}}{b^{2}}} = \frac{\sqrt{b^{2} - a^{2}}}{b}$ .

Final Answer: $\frac{\sqrt{b^{2} - a^{2}}}{b}$