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Understanding Sine, Cosine, and Tangent in Right Triangles

This resource introduces the fundamental concepts of trigonometric functions: sine, cosine, and tangent, as they relate to the parts of a right triangle. It covers key vocabulary like hypotenuse and legs, and explains how to calculate these ratios using given angles. Learn the famous mnemonic "SOH CAH TOA" to remember the definitions of sine, cosine, and tangent. The guide also provides steps for using calculators in degree mode and exercises to find sine, cosine, and tangent for specific angles, ensuring students grasp these essential trigonometric functions.

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Understanding Sine, Cosine, and Tangent in Right Triangles

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Presentation Transcript

  1. The Trigonometric Functions SINE COSINE TANGENT

  2. Parts of a Right Triangle Vocabulary B HYPOTNUSE LEG C A LEG

  3. Parts of a Right Triangle with 1 Given Angle B  C A HYPOTNUSE Opposite Adjacent

  4. hypotenuse hypotenuse opposite opposite A adjacent adjacent

  5. Or there’s the famous Indian Chief, Chief SOH CAH TOA Sin = Opp/Hyp Cos = Adj/Hyp Tan = Opp/Adj

  6. Finding sin, cos, and tan.(Just writing a ratio or decimal.)

  7. Find the sine, the cosine, and the tangent of angle A. Give a fraction and decimal answer (round to 4 places). 10.8 9 A 6 Shrink yourself down and stand where the angle is. Now, figure out your ratios.

  8. Find the sine, the cosine, and the tangent of angle A 24.5 Give a fraction and decimal answer (round to 4 decimal places). 8.2 A 23.1 Shrink yourself down and stand where the angle is. Now, figure out your ratios.

  9. Calculator time MODE • On your calculator, hit and third one down, make sure it is in “Degree” mode. If not, move over it and hit ENTER.

  10. Calculator TIME • Cos 76 degrees = • Sin 8 degrees =

  11. 8 32o y x Finding missing sides adj SOH CAH TOA Find x, two sides to use are hyp (H) and adj (A) hyp opp Use CAH (Cos)

  12. 8 32o y x Finding missing sides adj SOH CAH TOA Find y, two sides to use are opp (O) and adj (A) hyp opp Use TOA (Tan)

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