Find the Value Using the Unit Circle sin(20)

Problem

sin(20^∘)

Solution

1. Identify the angle and the unit. The task asks for the sine of 20 which is typically interpreted as 20^∘ in the context of introductory unit circle problems.

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

3. Recognize that 20^∘ is not a standard angle on the unit circle. Therefore, its sine 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. The sine of an angle in the first quadrant is the ycoordinate of the point on the unit circle.

5. Calculate the numerical value.

sin(20^∘)≈0.342020143

Final Answer

sin(20^∘)≈0.3420

Want more problems? Check here!