5.3
Apply 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:
sin A 
B
C
length of leg opposite A BC

length of hypotenuse
AB
length of leg adjacent A AC
cos A 

length of hypotenuse
AB
A
Sine and Cosine Ratios
O
S
H
OPPOSITE
A
C
H
ADJACENT
HYPOTENUSE
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.