Introduction to Trig Ratios

Introduction to Trig

Ratios

We use Trig Ratios for RIGHT TRIANGLES

We use Trig Ratios for RIGHT
TRIANGLES.

The first step is identifying the
REFERENCE ANGLE.

This angle is sometimes referred
to as theta 𝚹.

𝚹

Labeling/Identifying Sides

From the reference angle, you can
identify the sides of the triangle.

Hypotenuse: Longest side; across
from the right angle

*THESE 2 LABELS ARE DEPENDENT ON

THE REFERENCE ANGLE.*

Opposite: Leg ACROSS from the
reference angle.

Adjacent: Leg that makes the
angle.

Hypotenuse

𝚹

Opposite

Adjacent

Introduction to Trigonometry

​Opposite

𝚹

𝚹

𝚹

𝚹

𝚹

𝚹

𝚹

𝚹

𝚹

𝚹

​Opposite

​Adjacent

​Hypotenus

​Hypotenuse

​Adjacent

​Opposite

​Opposite

​Opposite

​Opposite

​Adjacent

​Adjacent

​Adjacent

​Hypotenuse

​Hypotenuse

​Hypotenuse

Multiple Choice

Which leg is opposite ∠F?

• $$\overline{DE}$$

• $$\overline{DF}$$

• $$\overline{EF}$$

• Cannot be determined

Multiple Choice

Which leg is adjacent to ∠F?

• $$\overline{DE}$$

• $$\overline{DF}$$

• $$\overline{EF}$$

• Cannot be determined

Multiple Choice

Which side is the hypotenuse?

• $$\overline{DE}$$

• $$\overline{DF}$$

• $$\overline{EF}$$

• Cannot be determined

Multiple Choice

What is the length of the side adjacent to ∠X?

• 7

• 24

• 25

Multiple Choice

What is the length of the hypotenuse?

• 16

• 30

• 34

Multiple Choice

Which side is opposite angle x?

• 1

• 2

• 3

Multiple Choice

Which side is the hypotenuse?

• 1

• 2

• 3

Multiple Choice

From ∠C, what side is AB?

• Adjacent

• Hypotenuse

• Opposite

Trig Ratios

Trig Ratios

​O

​H

​A 

𝚹

��

𝚹

𝚹

24

10

10

8

52

48

20

24

10

sin(𝚹)=
cos(𝚹)=
tan(𝚹)=

sin(𝚹)=
cos(𝚹)=
tan(𝚹)=

sin(𝚹)=
cos(𝚹)=
tan(𝚹)=

sin(𝚹)=
cos(𝚹)=
tan(𝚹)=

26

6

26

𝚹

��

𝚹

𝚹

24

10

10

8

52

48

20

24

10

sin(𝚹)=
cos(𝚹)=
tan(𝚹)=

sin(𝚹)=
cos(𝚹)=
tan(𝚹)=

sin(𝚹)=
cos(𝚹)=
tan(𝚹)=

sin(𝚹)=
cos(𝚹)=
tan(𝚹)=

26

6

26

​O

​O

​O

​O

​H

​H

​H

​H

​A

​A

​A

​A

​24/26 or 12/13

​10/26 or 5/13

24/10 or 12/5

20/52

48/52

20/48

8/10

6/10

8/6

26/24

10/24

26/10

Multiple Choice

Which is the correct ratio for the sine ratio?

• $$\frac{adjacent\ }{hypotenuse}$$

• $$\frac{opposite\ }{hypotenuse}$$

• $$\frac{adjacent\ }{opposite\ }$$

• $$\frac{opposite\ }{adjacent\ }$$

Multiple Choice

Which is the correct ratio for the cosine ratio?

• $$\frac{adjacent\ }{hypotenuse}$$

• $$\frac{opposite\ }{hypotenuse}$$

• $$\frac{adjacent\ }{opposite\ }$$

• $$\frac{opposite\ }{adjacent\ }$$

Multiple Choice

Which is the correct ratio for the tangent ratio?

• $$\frac{adjacent\ }{hypotenuse}$$

• $$\frac{opposite\ }{hypotenuse}$$

• $$\frac{adjacent\ }{opposite\ }$$

• $$\frac{opposite\ }{adjacent\ }$$

Multiple Choice

What is  $$\cos A$$  ?

• $$\frac{29}{20}$$  

• $$\frac{21}{29}$$  

• $$\frac{20}{29}$$  

• $$\frac{21}{20}$$  

Multiple Choice

What is  $$\tan A$$  ?

• $$\frac{29}{20}$$  

• $$\frac{21}{29}$$  

• $$\frac{20}{29}$$  

• $$\frac{21}{20}$$  

Multiple Choice

What is  $$\tan\ C$$  ?

• $$\frac{20}{21}$$  

• $$\frac{21}{29}$$  

• $$\frac{20}{29}$$  

• $$\frac{21}{20}$$  

Multiple Choice

cos______ = $$\frac{40}{50}$$  

• A

• B

• C

Multiple Choice

tan_____ =  $$\frac{30}{16}$$  

• X

• Y

• Z

Multiple Choice

sin _____ = $$\frac{16}{34}$$  

• X

• Y

• Z

Multiple Choice

Find the ratio for sinA. (Reduce the fraction)

• 36/27

• 4/5

• 36/45

• 3/5

Multiple Choice

What is the cosine of angle P?

• p/q

• q/r

• p/r

• r/q

Multiple Choice

If you are given the hypotenuse and an adjacent side, which trig function should you use?

• sine

• cosine

• tangent

• cotangent

Multiple Choice

If you are given the opposite side and hypotenuse, which trig function should you use?

• sine

• cosine

• tangent

Multiple Choice

Which trig function do you use?

• Sine

• Cosine

• Tangent

Multiple Choice

Which trig function do you use?

• Sine

• Cosine

• Tangent