TRIGONOMETRIC RATIOS Chapter 9.5. New Vocabulary  Trigonometric Ratio: The ratio of the lengths of two sides or a right triangle.  The three basic trigonometric.

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Presentation transcript:

TRIGONOMETRIC RATIOS Chapter 9.5

New Vocabulary  Trigonometric Ratio: The ratio of the lengths of two sides or a right triangle.  The three basic trigonometric ratios are SINE, COSINE, and TANGENT.  OPPOSITE??  ADJACENT??

Trigonometric Ratios Explained b a c C B A HYPOTENUSE Side ADJACENT to <A Side OPPOSITE <A

Trigonometric Ratios SINE (SOH) b a c C B A HYPOTENUSE Side ADJACENT to <A Side OPPOSITE <A Sin A = Side Opposite <A = O = a Hypotenuse H c

Trigonometric Ratios COSINE (CAH) b a c C B A HYPOTENUSE Side ADJACENT to <A Side OPPOSITE <A Cos A = Side Adjacent <A = A = b Hypotenuse H c

Trigonometric Ratios TANGENT (TOA) b a c C B A HYPOTENUSE Side ADJACENT to <A Side OPPOSITE <A Tan A = Side Opposite <A = O = a Side Adjacent <A A b

“ !”

What COLOR side is OPPOSITE <A? A

What COLOR side is ADJACENT TO <A? A

What COLOR side is the HYPOTENUSE? A

What is the sin of <X ? Y X Z

What is the tan of <Y ? Y X Z

What is the cos of <X ? Y X Z

What are the sin, cos, and tan of <H? H

Using a Calculator to Find Trigonometric Ratios for Specific Angles  You can find the trigonometric ratios for specific angles using a calculator…  Step 1: Make sure your calculator is in DEGREES!!! Go to MODE, and select degrees if necessary.  Step 2: Select the button for the trig. function you would like to use.  Step 3: Type the angle measure into the parenthesis.  Step 4: Close parenthesis and press enter!  Step 5: Round the answer to the desired number of decimal places.

Using a Calculator to Find Trigonometric Ratios for Specific Angles ROUND ANSWERS to four decimal places! Example 1: What is the sine of 25 degrees? Example 2: What is the tangent of 18 degrees? Example 3: What is the cosine of 49 degrees?