Track quiz
Eight quick questions, one for each idea. Use the table if you get stuck.
| Idea | Remember |
|---|---|
| Three ratios | In a right triangle, for acute A: sin A = opposite ÷ hypotenuse. cos A = adjacent ÷ hypotenuse. tan A = opposite ÷ adjacent. |
| Size does not matter | Angle A alone decides sin A, cos A and tan A. |
| The flips | cosec A = 1 ÷ sin A. sec A = 1 ÷ cos A. cot A = 1 ÷ tan A. |
| 0° and 90° | sin 0° = 0, cos 0° = 1, tan 0° = 0. sin 90° = 1, cos 90° = 0. tan 90° is not defined. |
| 45° | sin 45° = 1/√2. cos 45° = 1/√2. tan 45° = 1. |
| 30° and 60° | sin 30° = 1/2, cos 30° = √3/2, tan 30° = 1/√3. sin 60° = √3/2, cos 60° = 1/2, tan 60° = √3. |
| tan from sin and cos | tan A = sin A ÷ cos A. cot A = cos A ÷ sin A. |
| The identity | sin²A + cos²A = 1 for every acute angle A. |
A ramp is 5 m long. It rises 3 m and its foot is 4 m out. Angle A is at the foot of the ramp. What is cos A?
Two kites fly over flat ground. Each string makes the same angle with the ground. Their strings are 10 m and 30 m. Each height is straight up. How do their sines compare?
cos A = 5/13. What is sec A?
What is sin 0° + cos 0° + tan 0°?
A square is folded along its diagonal. What is tan 45°?
Find sin 30° + cos 60°.
sin P = 5/13 and cos P = 12/13. What is tan P?
sin A = 8/17. What is cos A?
Chapter 8 is Introduction to Trigonometry. Next comes Some Applications of Trigonometry. It points these ratios at real heights and distances.