Explanation of the given formula

The given formula is sin Theta = c / √(C^2 + D^2), where C is the length of the side adjacent to the angle Theta, D is the length of the side opposite to the angle Theta and c is the length of the hypotenuse.

Finding the value of cos Theta

We know that cos Theta = adjacent side / hypotenuse = C / c.

To find the value of cos Theta, we can use the Pythagorean theorem, which states that C^2 + D^2 = c^2.

From this, we can write C^2 = c^2 - D^2 and substitute it in the formula for cos Theta.

cos Theta = C / c = √(c^2 - D^2) / c

Finding the value of tan Theta

We know that tan Theta = opposite side / adjacent side = D / C.

We can also use the Pythagorean theorem to find the value of D.

D^2 = c^2 - C^2

Substituting this in the formula for tan Theta, we get

tan Theta = D / C = √(c^2 - C^2) / C

Therefore, the value of cos Theta is √(c^2 - D^2) / c and the value of tan Theta is √(c^2 - C^2) / C.

Conclusion

In conclusion, the values of cos Theta and tan Theta can be found using the given formula for sin Theta and the Pythagorean theorem. It is important to understand the concepts of trigonometry and the relationships between the sides and angles of a right triangle to solve such problems.

Sin θ = c/√(c² + d²)
cos θ = d/√(c² + d²)
tan θ = c/d