s3 (3.2) trigonometry applications...
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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.
Daily Practice 17.12.14
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.)
Q3. State the equation of the line joining (-3, 1) and (2, 4)
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.
S3 (3.2) Trigonometry Applications N5.notebook May 22, 2015
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
The area of a triangle 6.1.2015
ab sin C
The area of a triangle 6.1.2015
Example 1: Find the area of this triangle
C
A
D380
19cm
37cm
Daily Practice 7.1.2015
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.
S3 (3.2) Trigonometry Applications N5.notebook May 22, 2015
The area of a triangle 7.1.2015
Example 2: Find the area of this triangle
U
T
S410
1.7m
Daily Practice 12.1.2015
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.
S3 (3.2) Trigonometry Applications N5.notebook May 22, 2015
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
Daily Practice 13.1.2015
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
Daily Practice 14.1.2015
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
S3 (3.2) Trigonometry Applications N5.notebook May 22, 2015
Sine Rule to find an angle
Example 1: Calculate the size of the angle LZK
17cm 22cm
490
K
L
Z
Sine Rule to find an angle
Example 2: Calculate the bearing of J from FN
F
J
T
73km48km
1170
Daily Practice 19.1.2015
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
S3 (3.2) Trigonometry Applications N5.notebook May 22, 2015
Daily Practice 20.1.2015
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
S3 (3.2) Trigonometry Applications N5.notebook May 22, 2015
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
Daily Practice 21.1.2015
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
S3 (3.2) Trigonometry Applications N5.notebook May 22, 2015
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.
Daily Practice 26.1.2015
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
S3 (3.2) Trigonometry Applications N5.notebook May 22, 2015
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
S3 (3.2) Trigonometry Applications N5.notebook May 22, 2015
Daily Practice 28.1.2015
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!
Daily Practice 2.2.15
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
Q4. State the equation of the line joining (-1, 0) and (2, 4)
D
CB 11m
15m1150
S3 (3.2) Trigonometry Applications N5.notebook May 22, 2015
Today we will be creating questions on trigonometry.
Homework Due!
Daily Practice 3.2.2015
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.
S3 (3.2) Trigonometry Applications N5.notebook May 22, 2015
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.
'DLO\ 3UDFWLFH 4 6ROYH [ [
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
Daily Practice 10.2.2015
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
Daily Practice 11.2.2015
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