Solving trig equation

Hi, when doing part b and solving, how do I know what range of values of θ I need?

The MS (in red) had only 4 solutions corresponding to the four θ values (presumably because of repeated roots)

Reply 1

mqb2766

Original post

by subbhy

Hi, when doing part b and solving, how do I know what range of values of θ I need?
The MS (in red) had only 4 solutions corresponding to the four θ values (presumably because of repeated roots)

Can you post the actual question? It looks like red is -pi/2..pi/2 whereas the black is 0..2pi?

Edit - its 2020 paper and asks for the distinct roots. For the black solutions, 3pi/14 and 11pi/14 would not be distinct (symmetry of sin about pi/2 = 7pi/14). Id guess the easiest/most natural way to ensure theyre distinct is to pick the monotonic increasing part of the sin() curve for which arcsin() is defined, so -pi/2..pi/2 which is what the ms must do.

If you drew the angles on a unit circle/cast it would correspond to the vertices of a regular heptagon with a horizontal bottom. The symmetry about pi/2 or the y-axis would be clear and the ms has selected the roots that lie in the right half plane (including pi/2). The 3 that lie strictly to the right of the y-axis are mirrored by 3 that lie strictly in the left half plane.

(edited 11 months ago)

Reply 2

subbhy

Ah I get it, thank you!

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