Question:
If \(\sin\theta=\frac{3}{5}\), then \(\cos\theta=\)
If \(\sin\theta=\frac{3}{5}\), then \(\cos\theta=\)
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If only \(\sin\theta\) is given and quadrant is not mentioned, then \(\cos\theta\) may have both positive and negative values.
Updated On: May 7, 2026
- \(\frac{4}{5}\) but not \(-\frac{4}{5}\)
- \(-\frac{4}{5}\) or \(\frac{4}{5}\)
- \(-\frac{4}{5}\) but not \(\frac{4}{5}\)
- \(\frac{3}{5}\) but not \(-\frac{3}{5}\)
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The Correct Option is B
Solution and Explanation
We are given
\[
\sin\theta=\frac{3}{5}.
\]
We know the identity:
\[
\sin^2\theta+\cos^2\theta=1.
\]
Substitute the value of \(\sin\theta\):
\[
\left(\frac{3}{5}\right)^2+\cos^2\theta=1.
\]
\[
\frac{9}{25}+\cos^2\theta=1.
\]
\[
\cos^2\theta=1-\frac{9}{25}.
\]
\[
\cos^2\theta=\frac{25}{25}-\frac{9}{25}.
\]
\[
\cos^2\theta=\frac{16}{25}.
\]
Taking square root:
\[
\cos\theta=\pm \frac{4}{5}.
\]
Since the quadrant of \(\theta\) is not given, \(\cos\theta\) can be positive or negative.
Therefore,
\[
\cos\theta=\frac{4}{5}\quad \text{or}\quad -\frac{4}{5}.
\]
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