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16. The value of sin² 5° + sin² 10° + sin² 15° + … + sin² 90° is equal to


explain in better way ok ​

Sagot :

Answer:

11.5

Step-by-step explanation:

Let think mathematically. We have a finite series.

sin² 5° + sin² 10° + sin² 15° + … + sin² 90° . Remeber that sin is a periodic function, and we also know that

[tex] \sin {}^{2} (45 + 45) = 1[/tex]

and

[tex] \sin {}^{2} (30 + 60) = 1[/tex]

also that

[tex] \sin {}^{2} (0 + 90) = 1[/tex]

I'm imying that two angles that add up to 90 will make cancel out to 1.

Our full series will be

Angle measures increasing by 5 so

85+5=1

80+10=1

75+15=1

70+20=1

65+25=1

60+30=1

55+25=1

50+30=1

sin^2(45) is the same as sin(45)sin(45)=1/2.

And sin^2(90)=1 So our value is 9.5

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