Question

The angle [θ₁] is located in quadrant [iii], and [sin(θ₁)=-12/13] . what is the value of [cos(θ₁)]? express your answer exactly.

Answer 1

To find the value of cos(θ₁), use the trigonometric identity cos²(θ) + sin²(θ) = 1. Substitute sin(θ₁) = -12/13 into the equation and solve for cos(θ₁). The value of cos(θ₁) is -5/13.

Step-by-step explanation:

To find the value of cos(θ₁), we need to use the trigonometric identity: cos²(θ) + sin²(θ) = 1

Given that sin(θ₁) = -12/13, we can substitute this value into the equation:

cos²(θ₁) + (-12/13)² = 1

cos²(θ₁) + 144/169 = 1

cos²(θ₁) = 1 - 144/169

cos²(θ₁) = (169 - 144)/169

cos²(θ₁) = 25/169

cos(θ₁) = ±√(25/169)

Since θ₁ is in the third quadrant, where cos is negative, the correct value for cos(θ₁) is -5/13.