Tag: general knowledge

Northamptonshire County Cricket Club has been known as the 'Steelbacks' since 2014, particularly in T20 competitions. This nickname references the local steel industry heritage. Carnegie is a brand name for another team, while Spitfires is used by Kent and Brown Caps by Surrey.

Surrey County Cricket Club uses 'Brown Caps' as one of their traditional nicknames, referring to their brown caps worn in the past. The other options are nicknames of other counties: Bears (Warwickshire), Foxes (Leicestershire), Outlaws (Nottinghamshire).

The tangent function is defined as tan x = sin x / cos x, which is the ratio of sine to cosine for the same angle. Options A and B are incorrect reciprocals, while D would be cotangent (cot x = cos x / sin x).

The Pythagorean identity states that sin²x + cos²x = 1 for any angle x. This is one of the fundamental identities in trigonometry derived from the unit circle definition. Options 0, 90, and -1 are incorrect values for this expression.

Cosine is an even function, meaning cos(-x) = cos x for all x. This symmetry property holds because cosine is based on the x-coordinate on the unit circle, which is unchanged by reflecting across the x-axis. Sine is odd (sin(-x) = -sin x).

The cosine addition formula is cos(x+y) = cos x cos y - sin x sin y. This is a fundamental trigonometric identity for expanding cosine of a sum. Option A has the wrong sign, B mixes sine and cosine incorrectly, and D just reorders the terms but still has the wrong sign.

cos 0° = 1 because at angle 0 on the unit circle, the point is (1, 0), and cosine represents the x-coordinate. This is a fundamental value in trigonometry. Options 0, -1, and -1/2 are incorrect.

The double-angle formula for sine is sin 2x = 2 sin x cos x. This identity can be derived from the sine addition formula sin(x+x) = sin x cos x + cos x sin x. Option B is missing the factor of 2, and the other options are incorrect.

sin(180° - x) = sin x due to the supplementary angle identity. In the second quadrant (angles 90° to 180°), sine is positive and has the same value as its supplement. This is related to the symmetry of the sine function.