5.3Apply the SINE and

COSINE ratios

We will look at the TANGENT ratio tomorrow!

Sine and Cosine Ratios Are trigonometric ratios for acute

angles that involve the lengths of a leg and the hypotenuse of a right triangle.

Sine and Cosine Ratios Let ΔABC be a right triangle with acute A.

The sine of A and cosine of A (written as sinA and cosA) are defined as follows:

AB

BCA

hypotenuse of lengthA opposite leg of length

sin

A

B

C

AB

ACA

hypotenuse of lengthA adjacent leg of length

cos

Sine and Cosine Ratios

H

AC

H

OS

OPPOSITE

HYPOTENUSE

ADJACENT

HYPOTENUSE

Find SINE ratios Find sinX and sinY. Write each answer as

a fraction and as a decimal rounded to four places (the ten-thousandth place)

Find COSINE ratios Find cosX and cosY. Write each answer as

a fraction and as a decimal rounded to four places.

Extra Practice Find sinA and sinB.

Extra Practice Find cosA and cosB.

Find side lengths using SINE and COSINE

Find x. Round to the nearest tenth.

Extra Practice Find the value of x. Round to the nearest

tenth.