Question

Find all angles θ between 0° and 180° satisfying the given equation. Round your answer to one decimal place. (Enter your answers as a comma-separated list.) sin(θ) = 5 6

Answer 1

56.44°, 123.56°

Explanation:

Given equation,

`sin(\theta)=(5)/(6)`

`\implies \theta = sin^(-1) ((5)/(6))`

`\implies \theta =56.4426902381\approx 56.44^(\circ)`

`\because 0^(\circ) \leq \theta \leq 180^(\circ)`

Sine is positive in both first and second quadrant,

Also 56.44° lies in first quadrant,

Thus, the value of
`\theta` in second quadrant =
`180^(\circ)-\theta`

= 180° - 56.44° = 123.56°,

Hence, the value of
`\theta` in the given equation are,

56.44° and 123.56°