The Circular Functions (14.2)

A reference angle, ’, is the smallest, positive degree measure from the terminal side to the x-axis. (x, y) r  ’ Use Pythagorean Theorem: x2 + y2 = r2 Note: x can be  and y can be  (depending on the Quadrant) Since r is the radius, it must be (+) because it is a length.

I. The Six Trigonometric Functions Cosine: cos  = x Secant: sec  = r r x Sine: sin  = y Cosecant: csc  = r r y Tangent: tan  = y Cotangent: cot  = x y x

II. Sine and Cosine If the terminal ray of angle  in standard position contains (x, y) on the unit circle, then cos  = x and sin  = y or (cos , sin ) = (x, y). b/c radius is always 1 -1 ≤ cos  ≤ 1 and -1 ≤ sin  ≤ 1 Look at x-values and y-values so far on the unit circle

A. Finding trig values using calculator: Example: Use a calculator. Round to the nearest four decimal places. a) Sin 45°  .7071 b) cos 20°  .9397 sin 45 enter cos 20 enter NOTE: Make sure your calculator is in degree mode.

B. Finding angles using trig values and a calculator: Example: If 0 <  < 90, what is ? Round angles to the nearest tenth. a) sin   0.5299 b) cos   0.7218 2nd sin .5299 enter You’re “undoing” sine  = 32.0 2nd cos .7218 enter  = 43.8 NOTE: Make sure your calculator is in degree mode.

I. The Six Trigonometric Functions Cosine: cos  = x Secant: sec  = r = 1 r x cos  Sine: sin  = y Cosecant: csc  = r = 1 r y sin  Tangent: tan  = y = sin  Cotangent: cot  = x = cos  x cos  y sin 

III. Using all Trig Functions