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.

Using your calculator…

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Use the calculator to find the following

Sin, Cos, Tan

A

B C

Let this angle be xOpposite

Hypotenuse

Adjacent

∠𝑥

A

B C

Let this angle be xOppositeHypotenuse

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

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

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:

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 °

Angle Ratio (AC:CB:BA) Sine(x) Cosine(x) Tangent(x)

30

45 1 : 1 :

60

A

B C∠𝑥

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

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

Refer to Worksheet

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

𝑠𝑖𝑛−1= 1𝑠𝑖𝑛False!

Example 4:

4cm

5 cm 3 cmFind

Recall the formula:

Solution:

𝑆𝑖𝑛 𝑥=3𝑐𝑚5𝑐𝑚

x

𝐴𝑟𝑐𝑠𝑖𝑛 3𝑐𝑚5𝑐𝑚=𝑥

Answer

Example 5:

12cm

13 cm 5 cmFind

Recall the formula:

Solution:

𝐶𝑜𝑠 𝑥=12𝑐𝑚13𝑐𝑚

x

𝐴𝑟𝑐𝑐𝑜𝑠 12𝑐𝑚13 𝑐𝑚=𝑥

Answer

Example 6:

12cm

13 cm 5 cm

Recall the formula: tan

Solution:

𝑇𝑎𝑛𝑥=5𝑐𝑚12𝑐𝑚

x

𝐴𝑟𝑐𝑡𝑎𝑛 5 𝑐𝑚12𝑐𝑚=𝑥

Answer

Find

WORKSHEET TIME!