Question

Use the table to find the value of the following.
Sin117°

Answer 1

`\sin 117^(\circ) \approx 0.8910`

Explanation:

Sine reaches upper bound when
`\theta = 90^(\circ)` and then decreases until reaches lower bound when
`\theta = 180^(\circ)`. By symmetry, we find the following fact:

`\sin 117^(\circ) = \sin (90^(\circ)+27^(\circ)) = \sin (90^(\circ)-27^(\circ))`

`\sin 117^(\circ) = \sin 63^(\circ)`

By information form table we find that:

`\sin 63^(\circ) \approx 0.8910`

Therefore, we conclude that value of the given angle is:

`\sin 117^(\circ) \approx 0.8910`