If  $$\sin \theta = \frac{3}{5}$$​, where $$0^\circ < \theta < 90^\circ$$​, find the value of  $$\cos \theta$$​.

Correct option is A

If sin $$\theta = \frac{3}{5}, where 0^\circ < \theta < 90^\circ,$$​ find the value of $$\cos \theta$$​.

Solution

1. Given

​$$\sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}}$$​

From $$\sin \theta = \frac{3}{5}$$​:

​$$\text{Opposite} = 3, \quad \text{Hypotenuse}$$​ = 5

2. Using the Pythagorean Theorem:

​$$\text{Hypotenuse}^2 = \text{Opposite}^2 + \text{Adjacent}^2$$​

Substitute values:

​$$5^2 = 3^2 + \text{Adjacent}^2$$​

​$$25 = 9 + \text{Adjacent}^2$$​

​$$\text{Adjacent}^2 = 16 \quad \Rightarrow \quad \text{Adjacent} = 4$$​

3. Find $$\cos \theta$$​:

​$$\cos \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}}$$​

Substitute values:

​$$\cos \theta = \frac{4}{5}$$​

Final Answer

​$$\cos \theta = \frac{4}{5}$$​