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State whether the following are true or false. Justify your answer.

(i) The value of tan A is always less than 1.
(ii) sec A = 12/5 for some value of angle A.
(iii) cos A is the abbreviation used for the cosecant of angle A.
(iv) cot A is the product of cot and A.
(v) sin θ = 4/3 for some angle θ.

Mathematics - Mathematics



(i) False because tanα = perpendicular/base and perpendicular and base could be 5, 12 which leads to tanα = 5/12
(ii)True because sec A is the reciprocal of cos A, and the cos A is always between -1 and 1, this implies that sec A cannot be between -1 and 1, so 12/5 is possible
(iii) False because cos A is the abbreviation of cosine A
(iv) false because cot A is a single term not the product of cot and A
(v) False because the maximum value of sin α = 1 (sin90 = 1), therefore it cannot exceed 1.

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