Please help me!!! Will give brainliest and 12 points! Topic is Pythagorean identity find values

Answer:
cos θ = -(√3)/2
tan θ = -1/√3
Step-by-step explanation:
[tex]\frac{\pi }{2} <\theta <\pi \ \ \ sin \ \theta = \frac{1}{2} \\[/tex]
Part A: find cos θ:
Using Pythagorean identity
sin²θ + cos²θ = 1
cos²θ = 1 - sin²θ = 1 - (1/2)² = 1 - 1/4 = 3/4
cos θ = ±√(3/4) = ±(√3)/2
∵(π/2) < θ < π ⇒ ∴ cos θ = -(√3)/2
Part B: find tan θ:
sec θ = 1/(cos θ) = -2/√3
Using Pythagorean identity
tan²θ + 1 = sec²θ
tan²θ = sec²θ - 1 = 4/3 - 1 = 1/3
tan θ = ±√(1/3) = ± 1/√3
∵(π/2) < θ < π ⇒ ∴ tan θ = -1/√3