The graph of y=\sin ^2 x+\sin ^4 x+\sin ^6 x+\sin ^8 x+\cdots is sketched in

Oxford University MAT 2019 Solved Papers

Question : 3 of 10

Marks: +1, -0

The graph of

y=\sin ^2 x+\sin ^4 x+\sin ^6 x+\sin ^8 x+⋯

is sketched in

Solution:

When

x=0, y=0+0+0+⋯=0

. When

x=90^{∘}, y=1+1+1+. . .

diverges. Alternatively, note that this is a geometric series, with sum

\sin ^2 x \/(1-\sin ^2 x)=\tan ^2 x

Go to Question:

Prev Question

Next Question