Download - 5.3 Apply the SINE and COSINE ratios We will look at the TANGENT ratio tomorrow!

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Page 1: 5.3 Apply the SINE and COSINE ratios We will look at the TANGENT ratio tomorrow!

5.3Apply the SINE and

COSINE ratios

We will look at the TANGENT ratio tomorrow!

Page 2: 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.

Page 3: 5.3 Apply the SINE and COSINE ratios We will look at the TANGENT ratio tomorrow!

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

Page 4: 5.3 Apply the SINE and COSINE ratios We will look at the TANGENT ratio tomorrow!

Sine and Cosine Ratios

H

AC

H

OS

OPPOSITE

HYPOTENUSE

ADJACENT

HYPOTENUSE

Page 5: 5.3 Apply the SINE and COSINE ratios We will look at the TANGENT ratio tomorrow!

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)

Page 6: 5.3 Apply the SINE and COSINE ratios We will look at the TANGENT ratio tomorrow!

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

a fraction and as a decimal rounded to four places.

Page 7: 5.3 Apply the SINE and COSINE ratios We will look at the TANGENT ratio tomorrow!

Extra Practice Find sinA and sinB.

Page 8: 5.3 Apply the SINE and COSINE ratios We will look at the TANGENT ratio tomorrow!

Extra Practice Find cosA and cosB.

Page 9: 5.3 Apply the SINE and COSINE ratios We will look at the TANGENT ratio tomorrow!

Find side lengths using SINE and COSINE

Find x. Round to the nearest tenth.

Page 10: 5.3 Apply the SINE and COSINE ratios We will look at the TANGENT ratio tomorrow!

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

tenth.