Questions
 If tan x^{º} = ^{12}/_{5} and x is a reflex angle, find the value of 5sinx + cos x without using a calculator or mathematical tables
 Find θ given that 2 cos 3θ 1 = 0 for 0^{º} ≤ θ ≤ 360^{º}
 Without a mathematical table or a calculator, simplify:
giving your answer in rationalized surd form.  Express in surds form and rationalize the denominator.
 Simplify the following without using tables;
Tan 45 + cos 45sin 60  Simplify the following surds in the form of a + √b c where a, b, and c are constants
 John cycles from shopping centre A on a bearing of 120^{º} for 5 km to shopping centre B. He then cycles on a bearing of 200^{º} for 7 km to the shopping centre C. Calculate to 1 decimal place.
 The direct distance from A to C.
 The bearing of A from C.
 Bearing of B from C.
Answers
5 sin x + cos x
= 5 (^{12}/_{13}) − ^{5}/_{13}= ^{60}/_{13} − ^{5}/_{13} = ^{55}/_{13}= ^{12}/_{13 }




 b^{²} = a^{²} + c^{²} – 2ac cos B
b^{²} = 7^{²} + 5^{²} – 2.5.. 7 cos 100
= 74 – 70(0.173648)
= 74 + 12.15537
b² = 86.15537
b = 9.28199
AC = 9.3 km  ^{9.3}/_{sin100} = ^{5}/_{sinθ}Sin θ = ^{5sin100}/_{9.3} = 0.529466
θ = 31.9694
θ ≃ 32^{º}
32 – 20 = 12^{º}
Bearing = 360^{º}  12^{º} = 348^{º}  020^{º }
 b^{²} = a^{²} + c^{²} – 2ac cos B
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