Final answer:
To find the angle θ given sin(θ) = 7/8 and θ is in the second quadrant, calculate the reference angle with arcsin(7/8) and then subtract from 180° because sine is positive in the second quadrant. Thus, θ is approximately 119°.
Step-by-step explanation:
The student's question asks how to find the angle θ given that sin(θ) = 7/8, with θ in the second quadrant. To find θ, we will use the inverse sine function, also known as arcsin. However, since θ is in the second quadrant, we must consider the principle that sine is positive in the first and second quadrants, and the range of the arcsin function is from -90° to 90°.
First, find the reference angle α in the first quadrant such that sin(α) = 7/8:
α = arcsin(7/8)
Since a calculator is typically used for this, assume α ≈ 61° given the range of arcsin.
Now, because θ is in the second quadrant, we calculate θ as 180° - α:
θ = 180° - 61° = 119°
Therefore, the angle θ is approximately 119°.