Trigonometry 1.pptx

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Trigonometry 1

Angles and trigonometry

Lesson 6 of 7

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Last Lesson and Before

Angles and trigonometry

Lesson 6 of 7

Answer each one, then check.

1

Last lesson: how far apart are (0, 0) and (6, 8)?

2

Solve x/4 = 3.

3

Solve 12/x = 3.

4

Round 6.8829 to 3 significant figures.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Last Lesson and Before - Answers

Angles and trigonometry

Lesson 6 of 7

1

Last lesson: how far apart are (0, 0) and (6, 8)?

10

2

Solve x/4 = 3.

x = 12

3

Solve 12/x = 3.

x = 4

4

Round 6.8829 to 3 significant figures.

6.88

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Learning Objectives

Angles and trigonometry

Lesson 6 of 7

1

Label the hypotenuse, opposite and adjacent sides from a given angle.

2

Know the sine, cosine and tangent ratios.

3

Choose the right ratio for a problem.

4

Find a missing side of a right-angled triangle.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Naming the Sides

Angles and trigonometry

Lesson 6 of 7

Label from the angle you are using.

The hypotenuse is opposite the right angle. The opposite side is across from the angle θ. The adjacent side is next to θ and is not the hypotenuse. Move the angle and the opposite and adjacent sides swap.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

SOH CAH TOA

Angles and trigonometry

Lesson 6 of 7

θ is the Greek letter theta, often used for an angle.

Ratio

Formula

Uses

Sine

sin θ= opp/hyp

Opposite and hypotenuse

Cosine

cos θ= adj/hyp

Adjacent and hypotenuse

Tangent

tan θ= opp/adj

Opposite and adjacent

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Finding a Missing Side

Angles and trigonometry

Lesson 6 of 7

The same five steps every time.

1

Label

Label the sides O, A and H from the given angle.

2

Choose

Tick the side you know and the side you want. The two letters pick the ratio: O and H - sine; A and H - cosine; O and A - tangent.

3

Write

Write the ratio with the numbers in, e.g. sin 35°= x/12.

4

Rearrange

If x is on top, multiply. If x is on the bottom, swap x and the trig value.

5

Calculate

Check your calculator is in degrees (D on the screen), then round.

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The Unknown on Top

Angles and trigonometry

Lesson 6 of 7

A right-angled triangle has hypotenuse 15 cm. Angle θ= 42°. Work out the side opposite θ, to 1 decimal place.

1

Known: H = 15. Wanted: O. O and H means sine

sin 42°= x/15

2

Multiply both sides by 15

x = 15 sin 42°

3

Calculate

x = 10.036…

ANSWER

10.0 cm

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Using Tangent

Angles and trigonometry

Lesson 6 of 7

A right-angled triangle has an angle of 55°. The side adjacent to it is 8 cm. Work out the side opposite the 55° angle, to 1 decimal place.

1

Known: A = 8. Wanted: O. O and A means tangent

tan 55°= x/8

2

Multiply by 8

x = 8 tan 55°

3

Calculate

x = 11.425…

ANSWER

11.4 cm

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

The Unknown on the Bottom

Angles and trigonometry

Lesson 6 of 7

A right-angled triangle has an angle of 23°. The side opposite it is 6 cm. Work out the hypotenuse, to 1 decimal place.

1

Known: O = 6. Wanted: H. O and H means sine

sin 23°= 6/x

2

x is on the bottom, so swap x and sin 23°

x = 6/(sin 23°)

3

Calculate

x = 15.355…

4

Check: the hypotenuse is the longest side

15.4 > 6

ANSWER

15.4 cm

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Key Terms

Angles and trigonometry

Lesson 6 of 7

Hypotenuse

The side opposite the right angle; the longest side.

Opposite

The side across from the angle being used.

Adjacent

The side next to the angle being used, which is not the hypotenuse.

Sine (sin)

sin θ= opp/hyp.

Cosine (cos)

cos θ= adj/hyp.

Tangent (tan)

tan θ= opp/adj.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Angles and trigonometry

Lesson 6 of 7

YOUR TASK

Trig Relay

12 minutes

In pairs. For each triangle, one partner labels the sides and chooses the ratio; the other writes the equation and calculates. Swap roles each time. (a) H = 10, angle 50°, find A. (b) A = 14, angle 36°, find O. (c) A = 25, angle 20°, find H. (d) H = 3, angle 12°, find O.

1

Label O, A, H.

2

Choose the ratio.

3

Rearrange and calculate.

WHAT A GOOD ANSWER SHOWS

(a) 10cos 50°= 6.43 (b) 14tan 36°= 10.17 (c) 25/(cos 20°) = 26.60 (d) 3sin 12°= 0.62, all to 2 decimal places.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Can I...?

Angles and trigonometry

Lesson 6 of 7

Label the hypotenuse, opposite and adjacent sides.

Recall SOH CAH TOA.

Choose the right ratio.

Find a side when it is on the top of the fraction.

Find a side when it is on the bottom of the fraction.

Check my calculator is in degrees.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Summary & Exam Focus

Label from the angle: hypotenuse, opposite, adjacent.

SOH CAH TOA picks the ratio.

x on top: multiply. x on the bottom: divide.

Degree mode, then round at the end.

EXAM FOCUS

Triangle ABC is right-angled at B. AB = 7 cm and angle ACB = 40°. Work out the length of BC. Give your answer to 3 significant figures. (3 marks)

Write the ratio with the numbers in before you rearrange - it is usually worth a method mark on its own, even if the calculator step goes wrong.

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