16. The value of sin² 5° + sin² 10° + sin² 15° + … + sin² 90° is equal to explain in better way ok
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explain in better way ok
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Answer:
11.5
Stepbystep 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