Lesson 13 of 14

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Eight quick questions, one for each idea. Use the table if you get stuck.

Introduction to Trigonometry — the ratios and the exact values
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?

The 30 m string gives the bigger sine
The 10 m string gives the bigger sine
They are equal

cos A = 5/13. What is sec A?

13/5
5/13
12/13

What is sin 0° + cos 0° + tan 0°?

Not defined
0
1

A square is folded along its diagonal. What is tan 45°?

1
1/√2
√2

Find sin 30° + cos 60°.

1/2
1
√3

sin P = 5/13 and cos P = 12/13. What is tan P?

5/12
12/5
13/5

sin A = 8/17. What is cos A?

9/17
15/17
8/15

Chapter 8 is Introduction to Trigonometry. Next comes Some Applications of Trigonometry. It points these ratios at real heights and distances.

Reveal every answer to finish this lesson.

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