Question

If sin theta = a/b then what is cos theta equal to

Answer 1

sinθ=a/b
∴, cosθ=√(1-sin²θ) [∵, sin²θ+cos²θ=1]
or, cosθ=√(1-a²/b²)
or, cosθ=√{(b²-a²)/b²}
or, cosθ=√(b²-a²)/b Ans.

Answer 2

Answer:

$cos\theta =\frac{\sqrt{(b^{2}-a^{2})}}{b}$

Step-by-step explanation:

Given $sin\theta = \frac{a}{b}$ ---(1)

We know the Trigonometric identity:

$\boxed {cos^{2}\theta=1-sin^{2}\theta}$

Now ,

$cos\theta = \sqrt{1-sin^{2}\theta}$

= $\sqrt{1-\left(\frac{a}{b}\right)^{2}}$

\* From (1)*\

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

= $\frac{\sqrt{(b^{2}-a^{2})}}{b}$

Therefore,

$cos\theta =\frac{\sqrt{(b^{2}-a^{2})}}{b}$

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