Question

Find cos(2π/3) I need help

Answer 1

We can use the cosine double angle formula to find cos(2π/3):

cos(2θ) = cos^2(θ) - sin^2(θ)

Letting θ = π/3, we get:

cos(2π/3) = cos^2(π/3) - sin^2(π/3)

Using the values of cosine and sine of π/3 (which are known), we have:

cos(2π/3) = (1/2)^2 - (√3/2)^2

Simplifying, we get:

cos(2π/3) = 1/4 - 3/4

cos(2π/3) = -1/2

Therefore, cos(2π/3) is equal to -1/2.

Answer 2

cos(2π/3) = cos(π/3 + π/3)

= cos²(π/3) - sin²(π/3)

= (1/2)² - (√3/2)²

= 1/4 - 3/4

= -2/4

= -1/2

Explanation:

here are the steps:

• Convert 2π/3 to degrees: 2π/3 * (180/π) = 120°
• Use the double angle formula for cosine: cos(2θ) = cos²(θ) - sin²(θ)
• Substitute π/3 for θ: cos(2π/3) = cos²(π/3) - sin²(π/3)
• Use the values of cosine and sine of π/3 from the unit circle: cos(π/3) = 1/2 and sin(π/3) = √3/2
• Substitute these values into the formula: cos(2π/3) = (1/2)² - (√3/2)²
• Simplify the expression inside the parentheses: cos(2π/3) = 1/4 - 3/4
• Combine like terms: cos(2π/3) = -2/4
• Simplify the fraction: cos(2π/3) = -1/2

Therefore, cos(2π/3) = -1/2