F3 Mathematics Trigonometric Ratios Lesson

F3 Mathematics

Trigonometric Ratios Lesson

by Karla Williamson

​What is Trigonometry?

​Trigonometry is the branch of mathematics which deals with the relations of the sides and angles of triangles.

Labelling Right-Angled Triangles​

​Labelling Right-Angled Triangles

​The hypotenuse is ALWAYS the longest side.

​The opposite and adjacent sides depend on the angle being considered

(not the right angle).

Multiple Choice

In relation to the angle θ, label the side marked a in this right-angled triangle.

• Hypotenuse

• Adjacent

• Opposite

Multiple Choice

In relation to the angle θ, label the side marked b in this right-angled triangle.

• Hypotenuse

• Adjacent

• Opposite

Multiple Choice

In relation to the angle θ, label the side marked c in this right-angled triangle.

• Hypotenuse

• Adjacent

• Opposite

Multiple Choice

In relation to the angle θ, label the side marked c in this right-angled triangle.

• Hypotenuse

• Adjacent

• Opposite

Multiple Choice

Which side of the triangle is opposite of angle R?

• QP

• QR

• RP

Multiple Choice

Which side of the triangle is the hypotenuse?

• QP

• QR

• RP

Multiple Choice

The hypotenuse is always across from the right angle of a triangle.

• False

• True

Class work/Homework​

​Labelling the triangle

Page 188

​Ex. 10a # 1 - 6

The Trigonometric Ratios​

​Trigonometric Ratios

​The ratios of the sides of a right triangle are called trigonometric ratios. Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).

​Sin, Cos, Tan

​In these definitions, the terms opposite, adjacent, and hypotenuse refer to the lengths of the sides.

SOH-CAH-TOA​

​The word sohcahtoa helps us remember the definitions of sine, cosine, and tangent. Here's how it works:

Marked ​Assignment

• ​Create a poster which shows the Trigonometric Ratios.​

• ​Create an mnemonic which can make it easier to remember the ratios.

​

​e.g. Some Old Horses Can Always Hear Their Owner's Approach

​

​Due date will be posted on Classroom

​Practice Identifying Sides and Ratio

Multiple Choice

What side is x?

• opposite
• hypotenuse
• adjacent
• cosine

Multiple Choice

What side is x?

• adjacent
• opposite
• sine
• hypotenuse

Multiple Choice

SOH, CAH or TOA?

• SOH

• CAH

• TOA

Multiple Choice

SOH, CAH or TOA?

• SOH

• CAH

• TOA

Multiple Choice

SOH, CAH or TOA?

• SOH

• CAH

• TOA

Multiple Choice

SOH, CAH or TOA?

• SOH

• CAH

• TOA

Finding an Unknown Side

​Class work/Homework

​Finding an Unknown Side

​

​Ex. 10i

​Pages 200 - 201

​#19 - 36

​(multiples of 3)

​Practice - choosing the correct ratio and writing the ratio properly

Multiple Choice

What is the correct trig function?

• Sine

• Cosine

• Tangent

Multiple Choice

Choose the correct trig function

• Sine

• Cosine

• Tangent

Multiple Choice

Choose the correct trig function

• Sine

• Cosine

• Tangent

Multiple Choice

Choose the correct trig function

• Sine

• Cosine

• Tangent

Multiple Choice

Choose the correct trig funtion

• Sine

• Cosine

• Tangent

Multiple Choice

Choose the correct trig function

• Sine

• Cosine

• Tangent

Multiple Choice

Find the value of cos C.

• 29/20
• 21/20
• 20/29
• 20/21

Multiple Choice

Find the value of sin A.

• 3/4
• 5/4
• 5/3
• 4/5

Multiple Choice

Which ratio would be used to solve for x?

• cosine
• tangent
• sine
• adjacent

Multiple Choice

Which ratio would you use to solve for x?

• sine
• cosine
• hypotenuse
• tangent

Multiple Choice

Which equation would you use to solve for x?

• sin 62 = 10/x
• tan 62 = 10/x
• tan 62 = x/10
• cos 10 = x/62

Multiple Choice

Which equation would you use to solve for x?

• sin 58 = x/19
• cos 58 = x/19
• sin 58 = 19/x
• cos 58 = 19/x

​Practice - finding an unknown side

Multiple Choice

Solve for x.

• 8
• 14
• 19.8
• 9.9

Multiple Choice

Solve for x.

• 8
• 15.1
• 6.5
• 18.7

Multiple Choice

 Find side AB?

• 20 m
• 5 m
• 11.54 m
• 8.66 m

Multiple Choice

Find the length of side w.

• 21.4 cm
• 18.0 cm
• 36.5 cm
• 43.6 cm

Multiple Choice

Solve for x.

• 24.20
• 4.92
• 290.4
• 29.75

Multiple Choice

Solve for x.

• 10
• 11.3
• 12.0
• 15.0