Calculate sin^2 (6)+cos^2 (12)+cos^2 (48)+sin^2 (66)
To calculate the expression sin^2 (6)+cos^2 (12)+cos^2 (48)+sin^2 (66), you need to know how to calculate trigonometric functions. Here's a step-by-step process to help you calculate the expression:
1. Convert the given angles from degrees to radians. Trigonometric functions in most mathematical calculators work with radians.
- 6 degrees = 6 * (π/180) radians
- 12 degrees = 12 * (π/180) radians
- 48 degrees = 48 * (π/180) radians
- 66 degrees = 66 * (π/180) radians
2. Use your calculator to find the sine and cosine of each angle:
- sin(6) = sin(6 * (π/180))
- cos(12) = cos(12 * (π/180))
- cos(48) = cos(48 * (π/180))
- sin(66) = sin(66 * (π/180))
3. Square each value obtained:
- sin^2(6) = [sin(6)]^2
- cos^2(12) = [cos(12)]^2
- cos^2(48) = [cos(48)]^2
- sin^2(66) = [sin(66)]^2
4. Substitute the calculated values into the expression:
- sin^2(6) + cos^2(12) + cos^2(48) + sin^2(66) = [sin(6)]^2 + [cos(12)]^2 + [cos(48)]^2 + [sin(66)]^2
5. Evaluate the expression using your calculator.
Please note that the calculated values of sin and cos may be decimal approximations, depending on the level of precision your calculator provides.