Respuesta :
Answer:
Cos(2115°) =1/√2
Sin(2115°) = -1/√2
Step-by-step explanation:
We have to find the values of Cos (2115°) and Sin (2115°).
Now, 2115° can be written as (23×90°+ 45°).
Therefore, the angle 2115° lies in the 4th quadrant where Cos values are positive and Sin values are negative.
Hence, Cos (2115°) = Cos(23×90° +45°) =Sin 45° {Since 23 is an odd number, so the CosФ sign will be changed to SinФ} =1/√2 (Answer)
Again, Sin (2115°) = Sin(23×90° +45°) = -Cos 45° {Since 23 is an odd number, so the SinФ sign will be changed to CosФ} = -1/√2 (Answer)
Now, the required reference angle is 45°. (Answer)
Considering a reference angle of 315º, we have that:
[tex]\cos{2115^\circ} = \frac{\sqrt{2}}{2}[/tex]
[tex]\sin{2115^\circ} = -\frac{\sqrt{2}}{2}[/tex]
How to find the reference angle?
To find the reference angle of an angle x > 360, we calculate the remainder of the division of x and 360, as one lap in the circle is of 360º.
In this problem, x = 2115º, and the remainder of the division is of 315º. Considering that the equivalent on the first quadrant is of 360 - 315 = 45º, and the signals of the sine and the cosine on the fourth quadrant, we have that:
[tex]\cos{2115^\circ} = \cos{315^\circ} = \cos{45^\circ} = \frac{\sqrt{2}}{2}[/tex]
[tex]\sin{2115^\circ} = \sin{315^\circ} = -\sin{45^\circ} = -\frac{\sqrt{2}}{2}[/tex]
More can be learned about reference angles at https://brainly.com/question/14910565
