Respuesta :

rvkacademic

Answer:

-0.258819045.......

Step-by-step explanation:

We can use a scientific calculator

For sin 345°, the angle 345° lies between 270° and 360° (Fourth Quadrant).

Since sine function is negative in the fourth quadrant, thus sin 345° value =  -0.258819045. . .  using a calculator

I hope that is the answer required. If not feel free to ask more questions on this via comments

Notes
Since the sine function is a periodic function, we can represent sin 345° as, sin 345 degrees = sin(345° + n · 360°), n = 1, 2, 3..

⇒ sin 345° = sin 705° = sin 1065°, and so on.

Answer:

[tex]\frac{1}{4}[/tex] ( [tex]\sqrt{2}[/tex] - [tex]\sqrt{6}[/tex] )

Step-by-step explanation:

using the trigonometric identity

• sin(a - b) = sinacosb - cosasinb

and the exact values

• sin45° = cos45° = [tex]\frac{\sqrt{2} }{2}[/tex]

• cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]

• sin30° = [tex]\frac{1}{2}[/tex]

given

sin345°

345° is in the 4th quadrant , where sin < 0

= - sin(360 - 345)°

= - sin15°

= - sin(45 - 30)°

= - (sin45°cos30° - cos45°sin30° )

= - ( [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] - ( [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{1}{2}[/tex] )

= - ([tex]\frac{\sqrt{6} }{4}[/tex] - [tex]\frac{\sqrt{2} }{4}[/tex] )

= - [tex]\frac{1}{4}[/tex] ( [tex]\sqrt{6}[/tex] - [tex]\sqrt{2}[/tex] )

= [tex]\frac{1}{4}[/tex] ([tex]\sqrt{2}[/tex] - [tex]\sqrt{6}[/tex] )

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