lesson 1: trigonometric functions of acute angles
DESCRIPTION
Lesson 1: Trigonometric Functions of Acute Angles. Done by: Justin Lo Lee Bing Qian Danyon Low Tan Jing Ling. Trigonometric Functions. The three main functions in trigonometry are Sine , Cosine and Tangent . They are often shortened to sin , cos and tan. - PowerPoint PPT PresentationTRANSCRIPT
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Lesson 1:Trigonometric Functions of Acute Angles
Done by:
Justin Lo
Lee Bing Qian
Danyon Low
Tan Jing Ling
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Trigonometric Functions
• The three main functions in trigonometry are Sine, Cosine and Tangent.
• They are often shortened to sin, cos and tan.
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Using your calculator…
http://www.shopperhive.co.uk/compare/casio-fx83gt-calculator-prices
Use the calculator to find the following
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Sin, Cos, Tan
A
B C
Let this angle be xOpposite
Hypotenuse
Adjacent
∠𝑥
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A
B C
Let this angle be xOpposite
Hypotenuse
Adjacent
∠𝑥
• "Opposite" is opposite to the angle x• "Adjacent" is adjacent (next to) to the
angle x• "Hypotenuse" is the longest line
Sine Function: sin(x) = Opposite / Hypotenuse
Cosine Function: cos(x) = Adjacent / Hypotenuse
Tangent Function: tan(x) = Opposite / Adjacent
SOHCAH TOA
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Example 1:
Line A = cm
Line B (Hypotenuse) = 2 cmLine C = 1 cm
Line C is opposite to angle Find sin
Recall the formula: SSolution:
Length of Line C (Opposite)
Length of Line B (Hypotenuse)
𝑆𝑖𝑛 30 °=1𝑐𝑚2𝑐𝑚
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Example 2:
Line A = cm
Line B (Hypotenuse) = 2 cmLine C = 1 cm
Line C is adjacent to angle Find
Length of Line C (Adjacent)
Length of Line B (Hypotenuse)
Recall the formula:
Solution:
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Example 3:
Find
Recall the formula:
Solution:
Line B (H
ypotenuse
) = cm
Line A = 1 cm
Line C = 1 cm
Length of Line A/C (Opposite)
Length of Line C/A (Adjacent)
𝑇𝑎𝑛 45 °=1𝑐𝑚1𝑐𝑚
45 °
45 °
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Angle Ratio (AC:CB:BA) Sine(x) Cosine(x) Tangent(x)
30
45 1 : 1 :
60
A
B C∠𝑥
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Note:
• Always draw a diagram to visualise if confused!
• What if the triangle is not right-angled? Can we still use sin, cos, tan?– Angle of reference– Applies to adjacent and opposite too– Dependent on angle not triangle
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Think…
• How far up a wall could Bob the Builder reach with a 30 foot ladder, if the ladder makes a 70° angle with the ground? (2d.p)
y 30
70 °
0.93969= y= 28.19
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Refer to Worksheet
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Inverse Trigonometric Functions• Just as the square root function is defined
such that y2 = x, the function y = arcsin(x) is defined so that sin(y) = x
Name Usual Notation
Definition Aka
Arcsine Y = arcsin x X= sin y
Arccosine Y= arccos x X= cos y
Arctangent Y= arctan x X= tan y
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𝑠𝑖𝑛−1=1𝑠𝑖𝑛False!
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Example 4:
4cm
5 cm 3 cmFind
Recall the formula:
Solution:
𝑆𝑖𝑛𝑥=3𝑐𝑚5𝑐𝑚
x
𝐴𝑟𝑐𝑠𝑖𝑛3𝑐𝑚5𝑐𝑚
=𝑥
Answer
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Example 5:
12cm
13 cm 5 cmFind
Recall the formula:
Solution:
𝐶𝑜𝑠 𝑥=12𝑐𝑚13𝑐𝑚
x
𝐴𝑟𝑐𝑐𝑜𝑠12𝑐𝑚13 𝑐𝑚
=𝑥
Answer
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Example 6:
12cm
13 cm 5 cm
Recall the formula: tan
Solution:
𝑇𝑎𝑛𝑥=5𝑐𝑚12𝑐𝑚
x
𝐴𝑟𝑐𝑡𝑎𝑛5 𝑐𝑚12𝑐𝑚
=𝑥
Answer
Find
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WORKSHEET TIME!