Find the Value Using the Unit Circle cos(40)

Problem

cos(40^∘)

Solution

1. Identify the angle and the required trigonometric function. The task is to find the value of cos(40^∘)

2. Determine if the angle is a standard value on the unit circle. The standard angles are typically multiples of 30^∘ or 45^∘ (e.g., 0^∘,30^∘,45^∘,60^∘,90^∘.

3. Recognize that 40^∘ is not a standard angle on the unit circle. Therefore, its exact value cannot be expressed using simple radicals like 1/2 or √(,3)/2

4. Approximate the value using a calculator or trigonometric tables if a decimal value is required.

Final Answer

cos(40^∘)≈0.7660

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