How to Find the Value of Sec x for a Given Angle x: A Step-by-Step Guide with Examples

Sec x

Sec x stands for the secant function in mathematics and is the reciprocal of the cosine function

Sec x stands for the secant function in mathematics and is the reciprocal of the cosine function.

Let’s explore how to find the value of sec x for a given angle x:

1. Start by understanding the unit circle. The unit circle is a circle with a radius of 1, centered at the origin of a coordinate plane. It is commonly used to visualize trigonometric functions.

2. Identify the angle x for which you want to find the secant value.

3. Draw a right triangle with one angle as x, and the hypotenuse on the unit circle. Place the triangle in the appropriate quadrant to ensure the angle and triangle are correctly aligned.

4. Find the adjacent side length in the triangle. The adjacent side is the side adjacent to the angle x.

5. Determine the value of the adjacent side, which corresponds to the x-coordinate of the point where the angle’s terminal side intersects the unit circle. This value depends on the quadrant in which the angle falls.

6. Use the Pythagorean theorem to find the length of the hypotenuse. Since the unit circle has a radius of 1, the hypotenuse in this case is also equal to 1.

7. Apply the definition of sec x, which is the reciprocal of the cosine function. Thus, sec x = 1/cos x.

8. Calculate the cosine value for angle x by dividing the length of the adjacent side by the length of the hypotenuse (cos x = adjacent side / hypotenuse).

9. Substitute the cosine value into the expression for sec x (sec x = 1 / cos x). This will give you the secant value for angle x.

10. Simplify the expression if necessary to get the final answer.

Remember, the secant function can return any real value, positive or negative, including zero. The value of sec x depends on the specific angle x, so make sure you correctly identify the quadrant in which x lies to determine the proper sign.

More Answers: