Given sin( heta) = 4/5 and heta is in the first quadrant, find sin(2 heta) and cos(2 heta).

Since $\theta$ is in the first quadrant, $\cos(\theta)$ is positive.

$$\cos(\theta) = \sqrt{1 - \sin^2(\theta)}$$ $$= \sqrt{1 - \left(\frac{4}{5}\right)^2}$$ $$= \sqrt{1 - \frac{16}{25}}$$ $$= \sqrt{\frac{25-16}{25}}$$ $$= \sqrt{\frac{9}{25}}$$ $$= \frac{3}{5}$$

Use the double angle formula $\sin(2\theta) = 2\sin(\theta)\cos(\theta)$.

$$\sin(2\theta) = 2 \left(\frac{4}{5}\right) \left(\frac{3}{5}\right)$$ $$= \frac{2 \times 4 \times 3}{5 \times 5}$$ $$= \frac{24}{25}$$

Use the double angle formula $\cos(2\theta) = \cos^2(\theta) - \sin^2(\theta)$.

$$\cos(2\theta) = \left(\frac{3}{5}\right)^2 - \left(\frac{4}{5}\right)^2$$ $$= \frac{9}{25} - \frac{16}{25}$$ $$= \frac{9-16}{25}$$ $$= -\frac{7}{25}$$

The final answers are $\boxed{\sin(2\theta) = \frac{24}{25}}$ and $\boxed{\cos(2\theta) = -\frac{7}{25}}$.