Verify approximation for specific angle

A question is this type if and only if it asks to test or verify that a small angle approximation works for a specific numerical angle value (e.g., 5° or 45°).

1 questions · Moderate -0.5

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OCR MEI Paper 3 2022 June Q11

3 marks Moderate -0.5

11 Show that, for the angle \(45 ^ { \circ }\), the formula \(\sin \theta \approx \frac { 4 \theta ( 180 - \theta ) } { 40500 - \theta ( 180 - \theta ) }\) given in line 28 gives the same approximation for the sine of the angle as the formula \(\sin x \approx \frac { 16 x ( \pi - x ) } { 5 \pi ^ { 2 } - 4 x ( \pi - x ) }\) given in line 23.