Contents...1 of 43 © Boardworks Ltd 2008 A A A A A A 7.4 Finding angles Contents S3 Trigonometry S3.5 Angles of elevation and depression S3.6 Trigonometry in 3-D S3.2 The three ...

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7.4 Finding angles

Contents

S3 Trigonometry

S3.5 Angles of elevation and depression

S3.6 Trigonometry in 3-D

S3.2 The three trigonometric ratios

S3.1 Right-angled triangles

S3.3 Finding side lengths

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The inverse of sin

sin θ = 0.5, what is the value of θ?

To work this out use the sin–1 key on the calculator.

sin–1 0.5 = 30°

sin–1 is the inverse of sin. It is sometimes called arcsin.

30° 0.5

sin

sin–1

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The inverse of sin

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The inverse of cos

Cos θ = 0.5, what is the value of θ?

To work this out use the cos–1 key on the calculator.

cos–1 0.5 = 60°

Cos–1 is the inverse of cos. It is sometimes called arccos.

60° 0.5

cos

cos–1

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The inverse of tan

tan θ = 1, what is the value of θ?

To work this out use the tan–1 key on the calculator.

tan–1 1 = 45°

tan–1 is the inverse of tan. It is sometimes called arctan.

45° 1

tan

tan–1

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4 steps we need to follow:

Step 1 Find which two sides we knowout of

Opposite, Adjacent and Hypotenuse.

Step 2 Use SOHCAHTOA to decide which one of

Sine, Cosine or Tangent ratio to use in this

question.

Step 3 For Sine calculate Opposite/Hypotenuse, for

Cosine calculate Adjacent/Hypotenuse or for

Tangent calculate Opposite/Adjacent.

Step 4 Find the angle from your calculator, using

one of sin-1, cos-1 or tan-1

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Finding angles

We are given the lengths of the sides opposite and adjacent to

the angle, so we use:

tan θ =opposite

adjacent

tan θ =8

5

= 57.99° (to 2 d.p.)

θ

5 cm

8 cm

θ = tan–1 (8 ÷ 5)

Find θ to 2 decimal places.

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Finding angles

We are given the lengths of the sides opposite and

hypotenuse to the angle, so we use:

sin θ =opposite

hypotenuse sin θ =2.5

5

= 30.00° (to 2 d.p.)

θ = sin–1 ( 2.5÷ 5)

Find θ to 2 decimal places.

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Finding angles

We are given the lengths of the sides opposite and adjacent to

the angle, so we use:

tan θ =opposite

adjacenttan θ =

300

400

= 36.87° (to 2 d.p.)

θ = tan–1 (300 ÷ 400)

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Finding angles

We are given the lengths of the sides hypotenuse and

adjacent to the angle, so we use:

cos θ =adjacent

hypotenusecos θ =

6750

8100

= 33.56° (to 2 d.p.)

θ = cos–1 (6750 ÷ 8100)

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Finding angles

We are given the lengths of the sides opposite and

hypotenuse to the angle, so we use:

sin θ =opposite

hypotenuse sin θ =18.88

30

= 39.00° (to 2 d.p.)

θ = sin–1 ( 18.88÷ 30)