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)

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

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

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

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

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 = =

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) =

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 6.4705 = x 6.5= x Round to the nearest tenth

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

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=17.6540 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)

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 8.9905 = x x= 37.2462 x= 32.0067 9.0 = x x = 37.2 x = 32.0