\(\sin\theta = \frac{3}{5}\)
\(\cos \theta = \frac{4}{5}\)
Hypotenuse of the second triangle is: \(\sqrt{24^2+7^2} = 25\)
\(\sin \alpha = \frac{7}{25}\)
\(\tan \alpha = \frac{7}{24}\)
This means:
\(\theta = \arcsin \frac{3}{5} ≈ 36.87\)
\(\alpha = \arcsin \frac{7}{25} ≈ 16.26\)
Now:
1. \(\sin 2\theta ≈ \sin 2(36.87) ≈ \sin73.74 = 0.96\)
2. \(\cos 2\theta ≈ \cos 2(36.87) ≈ \cos 73.74 = 0.28\)
3. \(\sin 2\alpha ≈ \sin 2(16.26) ≈ \sin 32.52 = 0.5376\)
4. \(\tan 2\alpha ≈ \tan 2(16.26) ≈ \tan 32.52 ≈ 0.6376\)
.
