Theory question 105
Trigonometry(a) Given that m = tan 30° and n = tan 45°, simplify, without using calculator, (m − n)/(mn), leaving the answer in the form p + √q.
(b) There are 20 women in a bus. 15 of them wear glasses and 10 wear wrist watches. If a woman is chosen at random from the bus, find the probability that she wears both glasses and wrist watch.
Show the model answer
Model answer
(a) m = 1/√3, n = 1
(m − n)/(mn) = (1/√3 − 1) ÷ (1/√3) = 1 − √3
So p = 1 and the surd part is −√3
(b) Assume every woman wears at least one: 15 + 10 − x = 20 → x = 5
P(both) = 5/20 = 1/4
Explanation
Dividing by 1/√3 is the same as multiplying by √3.