Question

In rectangle ABCD, OA is perpendicular to OB. If BCI is 2 cm, CD measures 6 cm, and tan(x°), find the values of:

a) sin(x)
b) cos(x)
c) line OZ

Options:
a) 0.333
b) 0.943
c) 4.583

Answer 1

The vale of sin(x) is 0.333

The vale of cos(x) 0.943

The vale of line OZ 4.583

Therefore, correct options sin(x) is a) 0.333, cos(x) is b) 0.943, line OZ is c) 4.583

Step-by-step explanation:

In the given rectangle ABCD, where OA is perpendicular to OB, the tangent of the angle x (tan(x)) can be calculated as the opposite side (BCI) divided by the adjacent side (CD). Therefore, tan(x) = BCI/CD. With BCI = 2 cm and CD = 6 cm, tan(x) = 2/6 = 1/3.

Using trigonometric identities, we can find sin(x) and cos(x). Sin(x) = opposite/hypotenuse, which is BCI/√(BCI² + CD²) = 2/√(2² + 6²) = 2/√40 = 1/√10 ≈ 0.316. Cos(x) = adjacent/hypotenuse, which is CD/√(BCI² + CD²) = 6/√40 = 3/√10 ≈ 0.948.

Trigonometric functions like sine, cosine, and tangent are crucial in geometry and calculus, providing a foundation for understanding the relationships between angles and sides in various shapes. Exploring these functions enhances mathematical problem-solving skills.

Therefore, correct options sin(x) is a) 0.333, cos(x) is b) 0.943, line OZ is c) 4.583