Answer: We can use the identity sin^2 ϕ + cos^2 ϕ = 1 to find sin ϕ:
- cos^2 ϕ + sin^2 ϕ = 1
- sin^2 ϕ = 1 - cos^2 ϕ
- sin ϕ = ±√(1 - cos^2 ϕ)
Since 3π/2 < ϕ < 2π, we know that sin ϕ < 0. Therefore, we can take the negative square root:
- sin ϕ = -√(1 - cos^2 ϕ)
- sin ϕ = -√(1 - 0.4626^2)
- sin ϕ ≈ -0.8865
To find tan ϕ, we can use the identity tan ϕ = sin ϕ / cos ϕ:
- tan ϕ = sin ϕ / cos ϕ
- tan ϕ = -0.8865 / 0.8861
- tan ϕ ≈ -0.9996
Therefore, the decimal approximations for sin ϕ and tan ϕ are approximately -0.8865 and -0.9996, respectively.