Aoife S.

asked • 01/06/21

sin (theta+48°) = cos 2theta. What is the second step to find theta? What does theta equal?

Any help with this would be greatly appreciated.

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Yefim S. answered • 01/06/21

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sin(ς + 48°) = cos2ς; sin(ς + 48°) = sin(90° + 2ς); sin(2ς + 90°) - sin(ς + 48°) = 0; 2cos(3ς/2 + 64°)sin(ς/2 + 21°) = 0; sin(3ς/2 + 64°) = 0; 3ς/2 + 64° = 180°n; ς = -128°/3 + 120°n, n = 0, ±1, ±2, ...ς

sin(ς/2 + 21°) = 0; ς/2 + 21° = 180°n, ς = - 42° + 360°n, n = 0, ±1, ±2, ..

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Daniel B.

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I believe you have a couple typos. If you do not mind, let me rewrite your solution; sin(ς + 48°) = cos2ς; sin(ς + 48°) = sin(90° + 2ς); sin(2ς + 90°) - sin(ς + 48°) = 0; 2cos(3ς/2 + 69°)sin(ς/2 + 21°) = 0; cos(3ς/2 + 69°) = 0; 3ς/2 + 69° = 90° + 180°n; ς = 14° + 120°n, n = 0, ±1, ±2, ..; sin(ς/2 + 21°) = 0; ς/2 + 21° = 180°n; ς = - 42° + 360°n, n = 0, ±1, ±2, ..;
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01/06/21

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