Evaluate the expression cos 22 degrees and sec 22 degrees
cos22 = 0.9272.
sec22 = 1/cos22 = 1/0.9272 = 1,0785.
To evaluate the expressions cos 22 degrees and sec 22 degrees, you can use a scientific calculator or reference a trigonometric table. However, let me explain how you can calculate these values from scratch using basic trigonometric concepts.
Cosine Function (cos):
Cosine is a trigonometric function that gives the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. To evaluate cos 22 degrees, follow these steps:
1. Start with a right triangle: Draw a right triangle, and label one of the acute angles as 22 degrees.
2. Determine the adjacent side and the hypotenuse: Identify the side adjacent to the 22-degree angle and the hypotenuse in the triangle.
3. Apply the cosine formula: Use the cosine formula, which states that cos(angle) = (adjacent side length) / (hypotenuse length).
4. Substitute the values: Plug in the lengths of the adjacent side and the hypotenuse into the formula.
5. Calculate the result: Divide the length of the adjacent side by the length of the hypotenuse to get the value of cos 22 degrees.
Secant Function (sec):
The secant of an angle is the reciprocal of its cosine value, so sec(angle) = 1 / cos(angle). To calculate sec 22 degrees, follow these steps:
1. Calculate cos 22 degrees: Use the steps mentioned above to calculate the value of cos 22 degrees.
2. Take the reciprocal: Divide 1 by the value obtained in step 1 to get the value of sec 22 degrees.
Using a calculator or trigonometric table might be quicker, but understanding the basic steps allows you to grasp the concept behind evaluating these trigonometric expressions.