ZIMSEC O-Level Trigonometric Functions — practice questions

1. An identity is a mathematical statement that equates one quantity with another. 2. Trigonometric identities let an expression be rewritten with sine and cosine ratios only. 3. That rewriting is what makes it possible to prove further identities and solve equations. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 6: Trigonometry_

1. The sine, cosine and area rules all work in triangles that have no right angle. 2. The sine rule is chosen when two angles and a side are given. 3. It is also chosen when two sides and an angle that is not between them are given. 4. The cosine rule is for two sides with the angle between them, or for all three sides. 5. The area rule is used to find area, not a missing side or angle. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 6: Trigonometry_

1. The area rule works in any triangle and needs no perpendicular height. 2. It gives half the product of two side lengths multiplied by the sine of the angle between them. 3. Multiply the two sides: 10 cm times 8 cm is 80 square centimetres. 4. Multiply by the sine of the included angle: 80 times 0.5 is 40 square centimetres. 5. Take half of that: half of 40 is 20 square centimetres. 6. The area of the triangle is therefore 20 square centimetres. 7. Answering 80 square centimetres uses neither the sine value nor the halving. 8. Answering 40 square centimetres forgets the halving, and 18 square centimetres adds the sides instead. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 6: Trigonometry_