s3 (3.2) trigonometry applications...

S3 (3.2) Trigonometry Applications N5.notebook May 22, 2015

Daily Practice 16.12.14

Q1. Calculate the circumference of a circle with a radius of 5cm

Q2. Solve the equation 2(x - 1) = 3x + 4

Q3. State the equation of the line joining (3, -2) and (5, 4)

Q4. Calculate the height of a cylinder with volume 4162cm3 and a radius of 6cm

Today we will be working in groups to makes posters that show all the significant aspects of the straight line and scattergraphs.


Q1. Round 89.66 to the nearest unit

Q2. Calculate the area of a circle with diameter 15.7m

Q3. Calculate the length of x

Q4. Solve the equation 9(3x - 4) + 17 = 13(2x + 1)

Q5. State the equation of the line joining (-1, 4) and (2, 3)

13cm

12cm

xcm

Task

• In your groups, create a poster covering all the significant aspects of the straight line and the equation of the line of best fit.

• Use examples that you have made up yourselves.

• When you have this completed, redo your homework in your classwork jotter and using the graph paper. Work together to solve all the questions.

Daily Practice 6.1.15Q1. How much is an antique that was purchased for £350 and increased in value by 24% now worth?

Q2. Calculate the volume of a cylinder with diameter of base 8cm and height 14cm. (Give your answer to 2 s.f.)


Q4. Calculate the mean of 2, 3, 4, -5, 8, 0

Q5. 48 - (-15)

Today we will be learning how to calculate the area of a triangle given two sides and the included angle.


The area of a triangle 6.1.2015Calculate the area of this triangle

570

13cm

24cm

h

Step 1: Find h

Sin 57 = h

13 x Sin 57 = h

h = 10.9cm

13

Step 2: Find Area

A = 1/2 B x H

A = 0.5 x 24 x 10.9

A = 130.8cm2

Notice that Sin C = h

so aSinC = h

We know

Area = 0.5 base x height

=> 0.5 x b x h

but h = aSinC

so Area = 0.5abSinC

A0

c

b

ha

B0

C0

The area of a triangle 6.1.2015

12

Half of the product of the two sides multiplied by the sin of the angle in between

Area of a triangle =

A

B

C

c a

b


ab sin C


Example 1: Find the area of this triangle

C

A

D380

19cm

37cm


Q1. Calculate the current value of a house that was worth

£126 000 and dropped in value by 3.2% in its first year but rose by 4.5% in its second

Q2. State the equation of the line joining (2, 50) and (7, 75)

Q3. Calculate the standard deviation of 3, 4, 5, 7, 1

Today we will be continuing to calculate the area of a triangle using trigonometry.



Example 2: Find the area of this triangle

U

T

S410

1.7m


Q1. Calculate the height of a cylinder that has a diameter of 18cm and a volume of 6240cm3 . Give answer to 2 s.f.

Q2. Write 67 000 000 000 in scientific notation

Q3. Calculate the value of a painting purchased for £600 and appreciated in value by 13% in its first year and 17% in its second

Q4. Solve 3(4x - 1) + 2x = 13x + 7

Today we will be learning how to calculate the length of a side of a triangle that isn't right-angled.

Calculate x

380 310

23cm xcm

The Sine Rule

A

BCa

bc

The Sine Rule: Used when looking for a side in a triangle (not - right angled)

a bSinA SinB=

In words:

The side I need over the Sin of the angle across from it is equal to the side I know over the Sin of the angle across from it.


Example 1: Calculate the length of side LM

24cm

580

490

K

L

M

Sine Rule

Example 2: Calculate the length of side AC

Sine Rule

7.2cm1010

340

A

B

C


Q1. Calculate the area of this semi-circle

Q2. Calculate the length of p

Q3. Calculate the area of this triangle

Q4. A car purchased for £13 000 depreciated by 7% in its first year and 4.5% in its second, how much is it now worth?

14cm

8cm

p cm

460

1240

19cm

22cm


Q1. State the equation of the line joining (3, ‐4) and (4, 5)

Q2. How much did a jar that now weighs 475grams with 25% extra free

originally weigh?

Q3. Jenny records her running times each week

For week 1, Jenny got a mean time of 43minutes and a standard deviation

of 2.5. For week 2, Jenny got a mean time of 41 minutes and a standard

deviation of 4.8.

Make two comments comparing the above

L.I: Today we will be working out how to find the size of a missing angle in a triangle.

Use the same rule, just flip the formula upside down

SinA SinB

=a b

In words:

The sin of the angle I want over the side across from it is equal to the sin of the angle I know over the side across from it.

Sine Rule to find an angle



Example 1: Calculate the size of the angle LZK

17cm 22cm

490

K

L

Z


Example 2: Calculate the bearing of J from FN

F

J

T

73km48km

1170


20 Questions Mental Maths

L.I: Today we will be completing mixed Sine Rule Questions and questions in context.

Homework Online due 26.1.15



Q1. Jerry bought a car for £2300 and sold it for £1800. Calculate the perecntage loss

Q2. Draw the resultant vector 2a - b when a = and b =

Q3. Calculate the area of the triangle shown

Q4. Calculate the length of x13cm

17cm1480

22cm

840

xcm

510


Today we are going to learn about the Cosine Rule.

Homework Due Monday 26.1.15

Cosine Rule 20.1.15

We use the Cosine Rule when:

• We have 2 sides and the included angle and need to find the side opposite.

• We have all three sides and need to find an angle.

a2 = b2 + c2 - 2bcCosA

Side that you need

Angle opposite

the side you need.

Cosine Rule 20.1.15

Examples:

1. Calculate the length of the side kk m

6.5m

7.2m1210


Q1. Multiply out and simplify 3(2x + 1) + 5x(2x + 1)

Q2. Factorise 5xk - 10k

Q3. Calculate the magnitude of the vector

Q4. Calculate the area of the triangle shown

Q5.

16cm

7cm1290

Today we will be continuing to learn about using the Cosine Rule to find a missing side.

Homework Due Monday 26.1.15


Cosine Rule 20.1.15

Examples:

2. Two ships leave Aberdeen harbour. One sails at a bearing of 0580

for 280km to Stavanger. The other sails to Leiden at a bearing of

1250 for 415km. How far apart are Stavanger and Leiden by sea?

Cosine Rule 21.1.15

Examples:

3.


Q1. Solve 3x + 4

Q2.

Q3. The population of a colony of bacteria is 17 000 000, a disinfectant spray was sprayed onto them and killed them at a rate of 74% per minute. How many minutes did it take the disinfectant to kill 99% of the bacteria?

2 = 11

Today we will be using the Cosine Rule to find a missing angle in triangle.

Homework Due!

Cosine Rule 26.1.15

We have all three sides and need to find an angle.

Angle that you need

side opposite

the angle you need.

CosA = b2 + c2 -2bc

a2

Cosine Rule 26.1.15

Examples:

1. Calculate the size of

angle ACB


Cosine Rule 26.1.15

2. Calculate the bearing of

Penicuik from Balerno

600

Balerno

N

Edinburgh

Penicuik

13.8km

13.3km

15.5km

Daily Practice 27.1.2015Q1. State the gradient of the ramp shown

Q2. Calculate the standard deviation of

Q3. Find 4/7 of 350

Q4. State the rule for the table below

Find K when A = 23

K 1 2 3 4 5

A 3 5 7 9 11

3m

0.6m

64 88 12 48 12 80 100 20 92 82 20 36

40 84 52 92 32 32 76 16 12

64

88

12

48

12

80

100

20

92

82

20

36

40

84

52

92

32

32

76

16

12

Mean = 52144

1296

1600

16

1600

784

2304

1024

1600

900

1024

256

144

1024

0

1600

400

400

576

1296

1600

12

36

-40

-4

-40

28

48

-32

40

-30

-32

-16

-12

32

0

40

20

-20

24

-36

-40

19588

Today we will be learning to complete questions on both the Sine and Cosine Rule and go through the homework.

Homework Online due 2.2.15



Q1. Calculate the area of this triangle. Give your answer to 2 s.f.

Q2. State the equation of the line joining (‐1, 4) and (2, 3)

Q3. State the gradient and y ‐ intercept of the line y = ‐x + 2

Q4. Calculate the length of m

5.6m2.3m880

36cm 42cm1250

m

Today you will be learning to make your own Trigonometry Questions.

Homework Due Monday!


Q1. Calculate the length of the side DC

Q2.

Q3. Calculate the value of an antique that was purchased for £450 and appreciated in value by 2.1% per annum for 4 years


D

CB 11m

15m1150


Today we will be creating questions on trigonometry.

Homework Due!


Q1. Calculate how much interest you would pay on a mortgage of £170 000 in 1 year if the rate is 4.7%APR

Q2. State the equation of the line joining (2, 8) and (3, 4)

Q3. Two forces are represented by the vectors

and . Find the resultant force

Q4. Calculate the length of AC

A

B

C

1180 28m19m

Today we will be continuing to work out mixed trigonometry questions.


Mixed Trigonometry Questions

When to use which rule:

Sine Rule

• When you need an angle, have 2 sides and an angle across from one of the sides.

• When you need a side, have 2 angles and one side across from 1 of the angles.

Cosine Rule

• When you need an angle and have all three sides

• When you need a side and have 2 sides and the included angle.

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4 ‒RKQ QRZ HDUQV i SHU PRQWK DIWHU JHWWLQJ D SD\ ULVH +RZ PXFK GLG KH HDUQ EHIRUH WKH SD\ ULVH"

4 &DOFXODWH WKH PDJQLWXGH RI ZKHQ

4 &DOFXODWH WKH DUHD RI WKH JDUGHQ

Today we will be completing a check-up on trigonometry


Q1. Calculate the original value of a house that is now worth £135000 after an increase of 4.6% this year

Q2. Calculate the magnitude of the vector

Q3. State the equation of the line joining (‐1, 3) and (2, 4)

Q4. Calculate the area of the triangle shown15cm

17cm380

Revision for Applications AssessmentStaon 1:

Pawel, Kirse, Fergus B, Amber, Nathan

Staon2:

Kae W, Jema, Jay‐Ger, Fergus C

Staon 3:

Emma, Kae L, Conor, Jake, Farah

Staon 4:

Robbie, Hannah, Joy, Ryan, Nicole,

Staon 5:

Jason, Emily, Sarah, Mahew, Rachel,

Staon 6:

Mairi, Stacey, Charloe, Finlay, Ben,

Revision for Unit 1 Test is online


Q1. Calculate the current value of a car that originally cost £11 000 and depreciated in value by 11.4%

Q2. State the equation of the line joining

(0, 4) and (3, 2) in the form y = mx + c

Q3. Calculate the size of the angle BYQ

B

Y

Q38cm

21cm 25cm

s3 (3.2) trigonometry applications...

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