9 5 Trigonometric Ratios Sine and Cosine Geometry

Goals n n Find the sine and cosine, of an acute angle. Solve problems

Right Triangle e t o p Hy A 03 October 2020 e s u

Trig Ratio Definition: Sine e t o p Hy A e s u n

Trig Ratio Definition: Cosine e t o p Hy A e s u n

Abbreviations Opposite A = Hypotenuse Sine sin of A Adjacent cos A Cosine of

Memory Aid n n n Sine is Opposite over Hypotenuse. Cosine is Adjacent over

Writing Ratios SOHCAHTOA ? ? ? 03 October 2020 ? B 5 3 4

Example 1 Find x. From the 28 angle, x is the ? Opposite side,

Example 1 Find x. Write the equation and solve. x 15 28 03 October

Example 2 Find y. Write the equation and solve. 56 31 y 03 October

Example 3 Find x. Write the equation and solve. 15 15 Cos 28 =

Example 4 Find y. Write the equation and solve. 56(Sine 31) = y y

Example 5 Find x. Write the equation and solve. x. COS 28 = 15

Summarize 03 October 2020 Geometry 9. 5 Trigonometric Ratios w/o Calculator 15

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9. 5 Trigonometric Ratios Sine and Cosine Geometry How do you Sine and Cosine ratios to find missing lengths of right triangles?

Goals n n Find the sine and cosine, of an acute angle. Solve problems using trigonometric ratios. 03 October 2020 Geometry 9. 5 Trigonometric Ratios w/o Calculator 2

Right Triangle e t o p Hy A 03 October 2020 e s u n Opposite Adjacent Geometry 9. 5 Trigonometric Ratios w/o Calculator 3

Trig Ratio Definition: Sine e t o p Hy A e s u n Opposite Adjacent Opposite Sine of A = Hypotenuse 03 October 2020 Geometry 9. 5 Trigonometric Ratios w/o Calculator 4

Trig Ratio Definition: Cosine e t o p Hy A e s u n Opposite Adjacent Cosine of A = Hypotenuse 03 October 2020 Geometry 9. 5 Trigonometric Ratios w/o Calculator 5

Abbreviations Opposite A = Hypotenuse Sine sin of A Adjacent cos A Cosine of A = Hypotenuse Opposite A = Adjacent Tangenttan of A 03 October 2020 Geometry 9. 5 Trigonometric Ratios w/o Calculator 6

Memory Aid n n n Sine is Opposite over Hypotenuse. Cosine is Adjacent over Hypotenuse. Tangent is Opposite over Adjacent. SOHCAHTOA 03 October 2020 Geometry 9. 5 Trigonometric Ratios w/o Calculator 7

Writing Ratios SOHCAHTOA ? ? ? 03 October 2020 ? B 5 3 4 Geometry 9. 5 Trigonometric Ratios w/o Calculator A ? ? ? 8

Example 1 Find x. From the 28 angle, x is the ? Opposite side, and 15 is the x Hypotenuse. What trig ratio is this? 15 28 Sine (SOHCAHTOA) 03 October 2020 Geometry 9. 5 Trigonometric Ratios w/o Calculator 9

Example 1 Find x. Write the equation and solve. x 15 28 03 October 2020 Geometry 9. 5 Trigonometric Ratios w/o Calculator 10

Example 2 Find y. Write the equation and solve. 56 31 y 03 October 2020 Geometry 9. 5 Trigonometric Ratios w/o Calculator 11

Example 3 Find x. Write the equation and solve. 15 15 Cos 28 = x 15(. 8829) = x 03 October 2020 28 x Geometry 9. 5 Trigonometric Ratios w/o Calculator 12

Example 4 Find y. Write the equation and solve. 56(Sine 31) = y y 56 31 56(. 515) = y 03 October 2020 Geometry 9. 5 Trigonometric Ratios w/o Calculator 13

Example 5 Find x. Write the equation and solve. x. COS 28 = 15 x 28 15 03 October 2020 Geometry 9. 5 Trigonometric Ratios w/o Calculator 14

Summarize 03 October 2020 Geometry 9. 5 Trigonometric Ratios w/o Calculator 15