Find tan(x) and cos(x) in the diagram. Find sin(θ) and cos(θ) in the diagram. Find the value of Γ sin(Γ) and cos(Γ).

Using the Pythagorean theorem, $a^2 + b^2 = c^2$:

The hypotenuse is 5.

$\tan(x) = \frac{\text{Opposite}}{\text{Adjacent}}$

$\cos(x) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$

The values are $\boxed{\tan(x) = \frac{3}{4}}$ and $\boxed{\cos(x) = \frac{4}{5}}$.

: Find $\sin(\theta)$ and $\cos(\theta)$
The diagram shows a right-angled triangle with the side opposite angle $\theta$ as 12 and the side adjacent to angle $\theta$ as 9.

Using the Pythagorean theorem, $a^2 + b^2 = c^2$:

The hypotenuse is 15.

$\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$

$\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$

The values are $\boxed{\sin(\theta) = \frac{4}{5}}$ and $\boxed{\cos(\theta) = \frac{3}{5}}$.

: Find the value of $\Gamma \sin(\theta)$ and $\cos(\theta)$
This question appears to refer to the same angle $\theta$ from the second diagram, as no new diagram is provided and $\Gamma$ is an undefined constant.

From , we found $\sin(\theta) = \frac{4}{5}$ and $\cos(\theta) = \frac{3}{5}$.

Since $\Gamma$ is an unknown constant, we express the value in terms of $\Gamma$:

The values are $\boxed{\Gamma \sin(\theta) = \frac{4\Gamma}{5}}$ and $\boxed{\cos(\theta) = \frac{3}{5}}$.