CSEE (Form 4) Trigonometric Functions — practice questions

1. The three sides of a right-angled triangle are named relative to the angle you are working with. 2. The hypotenuse is always opposite the right angle and is always the longest side. 3. It keeps that position whichever of the other two angles you choose to look at. 4. The opposite and adjacent sides do swap places when you switch angle. _Source: Siyavula Mathematics Grade 10 (Everything Maths, CC BY 4.0), Chapter 5: Trigonometry_

1. The tangent ratio is the opposite side divided by the adjacent side. 2. Neither of those two sides has to be the longest side of the triangle. 3. The opposite side can therefore be many times longer than the adjacent side. 4. So there is no maximum value for the tangent ratio. 5. Sine and cosine both divide by the hypotenuse instead, which is why they cannot exceed 1. _Source: Siyavula Mathematics Grade 10 (Everything Maths, CC BY 4.0), Chapter 5: Trigonometry_

1. The sides of a right-angled triangle obey the Theorem of Pythagoras. 2. The square of the hypotenuse equals the sum of the squares of the two other sides. 3. Square the first short side: 6 times 6 is 36. 4. Square the second short side: 8 times 8 is 64. 5. Add them: 36 plus 64 is 100. 6. The hypotenuse is the number whose square is 100, which is 10, so the hypotenuse is 10 cm. 7. Answering 14 cm just adds the two short sides, which ignores the theorem. 8. Answering 48 cm multiplies them, which is the area trap rather than a length. _Source: Siyavula Mathematics Grade 10 (Everything Maths, CC BY 4.0), Chapter 5: Trigonometry_