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

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Presentation transcript:

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: A B C

Sine and Cosine Ratios 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.