Periodicity and symmetry of trig functions

Questions that ask to express trig values at shifted angles (e.g. sin(θ + 180n)°, tan(θ + 180)°, tan 690°) in terms of the original trig value, using periodicity or symmetry properties.

3 questions · Moderate -0.9

1.05a Sine, cosine, tangent: definitions for all arguments

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OCR MEI C2 Q4

2 marks Moderate -0.8

4 The \(n\)th term, \(t _ { n }\), of a sequence is given by $$t _ { n } = \sin ( \theta + 180 n ) ^ { \circ }$$ Express \(t _ { 1 }\) and \(t _ { 2 }\) in terms of \(\sin \theta ^ { \circ }\).

OCR MEI C2 2011 June Q10

2 marks Easy -1.2

10 The \(n\)th term, \(t _ { n }\), of a sequence is given by $$t _ { n } = \sin ( \theta + 180 n ) ^ { \circ } .$$ Express \(t _ { 1 }\) and \(t _ { 2 }\) in terms of \(\sin \theta ^ { \circ }\).

OCR MEI AS Paper 2 2021 November Q3

3 marks Moderate -0.8

3 In this question you must show detailed reasoning. You are given that \(\tan 30 ^ { \circ } = \frac { 1 } { \sqrt { 3 } }\).
Explain why \(\tan 690 ^ { \circ } = - \frac { 1 } { \sqrt { 3 } }\).