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Published byAustin Robinson Modified over 8 years ago

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**A B C Warm UP What side is The hypotenuse? What side is opposite A?**

Line AB (purple) What side is opposite A? Line CB (red) What side is adjacent to A? Line AC (blue) What side is opposite B? Line AC (blue) What side is adjacent to B? Line CB (red)

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**SohCahToa Trigonometric Ratio The Ratio of two sides of a triangle**

There are 3 trigonometric ratios: Sine: Opposite over the hypotenuse Cosine: Adjacent over the hypotenuse Tangent: Opposite over the adjacent SohCahToa

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Sine (sin) Opposite Hypotenuse A C B CB Sin A = AB AC Sin B = AB

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Cosine (cos) adjacent Hypotenuse A C B AC Cos A = AB CB Cos B = AB

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Tangent (tan) Opposite adjacent A C B CB tan A = AC AC tan B = CB

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**Find the sine, cosine, and tangent of each angle**

B 12 16 20 16 20 4 5 sin A = = 20 12 5 3 Cos A = = 16 12 4 3 tan A = = Look at the sin of A and the cos of B. Do you notice anything? Look at tan A and tan B. 20 12 5 3 sin B = = 16 20 4 5 Cos B = = We will never do this with a right angle. 12 16 3 4 tan B = =

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Your calculator or a trig table gives you the trigonometric ratio for every possible angle of a triangle. Always make sure your calculator is set in degrees before starting any problem. Try these: ( round to 4 decimal places) Remember that these values represent the ratio of the sides of the triangle. sin 30° = cos 25° = tan 45° = sin 78° = 0.5 .9063 Opposite hypotenuse sin (A) = 1 Adjacent hypotenuse cos (A) = .9781 opposite adjacent tan (A) =

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If you know one side and an angle you can use the trigonometric ratio to find the other side by writing a proportion X is adjacent to the 75 degree angle and 25 is the hypotenuse so we will use Cosine x 75° 25 This doesn’t look like a proportion does it? X 25 cos 75= How about now? 1 25 cos 75 = x 25 (.2588) = x Using a calculator = x 6.5= x Round to the nearest tenth

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**Identify which trig function you would use to solve for the x**

6 65° x 25 20° x 16 25° sin cos tan 70° 35 x 32° 20 x sin tan cos 68° x 24

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**When the variable is on the bottom don’t panic!**

x 16 25° Remember when life was easy and you and you did problems like this: 4= 20 x cos 25= 16 x Multiply by x on both sides Put this in your calculator. x= 16 cos 25 4x = 20 Now divide by 4 on both sides x= x= 20 4 X =17.7 See how the x and the 4 just switch places. That always happens. (That’s what I love about math)

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**Now solve for x x 24 35 x 20 x cos 68= sin 70= tan 32= 35 sin 70**

70° 35 x 32° 20 x 68° x 24 sin 70= 35 x tan 32= 20 x cos 68= x 24 x= 20 tan 32 x= 35 sin 70 24 cos 68 = x = x x= x= 9.0 = x x = 37.2 x = 32.0

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