If \(\sin\theta = \dfrac{20}{29}\), then complete the following activity to find \(\cos\theta\).Activity : \(\sin^2\theta + \cos^2\theta = 1\)\(\left(\text{____}\right)^2 + \cos^2\theta = 1\)\(\dfrac{400}{841} + \cos^2\theta = 1\)\(\therefore \cos^2\…

Answer: the blanks are \(\dfrac{20}{29}\), \(\dfrac{400}{841}\), \(\dfrac{441}{841}\) and \(\cos\theta = \dfrac{21}{29}\).

Activity completed:

\(\sin^2\theta + \cos^2\theta = 1\)
\(\left(\dfrac{20}{29}\right)^2 + \cos^2\theta = 1\)
\(\dfrac{400}{841} + \cos^2\theta = 1\)
\(\therefore \cos^2\theta = 1 - \dfrac{400}{841}\)
\(\cos^2\theta = \dfrac{441}{841}\)
Taking square roots of both sides
\(\therefore \cos\theta = \dfrac{21}{29}\)

(\(\theta\) is acute, so the positive root is taken.)