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8-4 Trigonometry

Trigonometric Ratios The ratio of the lengths of two sides of a right triangle is called a

trigonometric ratio. The three most common ratios are sine, cosine, and tangent, which

are abbreviated sin, cos, and tan, respectively.

sin R =

leg opposite ∠𝑅

hypotenuse

cos R =

𝑟

leg adjacent to ∠𝑅

hypotenuse

𝑠

=𝑡

=𝑡

tan R =

leg opposite ∠𝑅

leg adjacent to ∠𝑅

𝑟

=𝑠

Example: Find sin A, cos A, and tan A. Express each ratio as a fraction and a

decimal to the nearest hundredth.

sin A =

opposite leg

hypotenuse

𝐵𝐶

= 𝐵𝐴

=

5

13

≈ 0.38

cos A =

adjacent leg

hypotenuse

𝐴𝐶

= 𝐴𝐵

=

12

13

≈ 0.92

tan A =

opposite leg

adjacent leg

𝐵𝐶

= 𝐴𝐶

=

5

12

≈ 0.42

Exercises

Find sin J, cos J, tan J, sin L, cos L, and tan L. Express each ratio as a fraction and as a decimal to the nearest

hundredth if necessary.

1.

2.

3.

Answers:

1.

𝟏𝟐

= 𝟎. 𝟔

𝟐𝟎

𝟏𝟔

𝒄𝒐𝒔𝑱 =

= 𝟎. 𝟖

𝟐𝟎

𝟏𝟐

𝒕𝒂𝒏𝑱 =

= 𝟎. 𝟕𝟓

𝟏𝟔

𝒔𝒊𝒏𝑱 =

𝟏𝟔

= 𝟎. 𝟖

𝟐𝟎

𝟏𝟐

𝒄𝒐𝒔𝑳 =

= 𝟎. 𝟔

𝟐𝟎

𝟏𝟔

𝒕𝒂𝒏𝑳 =

= 𝟏. 𝟑𝟑

𝟏𝟐

𝒔𝒊𝒏𝑳 =

2.

𝟐𝟒

= 𝟎. 𝟔

𝟒𝟎

𝟑𝟐

𝒄𝒐𝒔𝑱 =

= 𝟎...