Cos x = 0.789. Find sin x

Full Answer Section

1. Cos x value: We are given that cos x = 0.789. Locate the angle on the unit circle where the x-coordinate is 0.789. This angle is approximately 66.4 degrees (rounded to one decimal place).

2. Sine Relationship: Since sine and cosine are complementary angles on the unit circle, their relationship is sin(x) = cos(pi/2 - x).

3. Find sin x: Therefore, sin x = cos(pi/2 - 66.4°) = cos(23.6°).

4. Calculate sin x: Using a calculator, sin(23.6°) ≈ 0.704.

Answer: sin x ≈ 0.704

Sample Answer

Certainly! You can find sin x using the unit circle and trigonometric relationships. Here's how:

1. Unit Circle: The unit circle is a fundamental tool in trigonometry. It's a circle centered at the origin (0,0) with a radius of 1. The cosine (cos) of an angle is represented by the x-coordinate of a point on the circle, and the sine (sin) is represented by the y-coordinate of that point.