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 = r2Note: x can be and y can be (depending on the Quadrant)Since r is the radius, it must be (+) because it is a length.
3 I. The Six Trigonometric Functions Cosine:cos = xSecant:sec = rrxSine:sin = yCosecant:csc = rryTangent:tan = yCotangent:cot = xyx
4 II. Sine and CosineIf 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 ≤ 1Look at x-values and y-values so far on the unit circle
5 A. Finding trig values using calculator: Example:Use a calculator. Round to the nearest four decimal places.a) Sin 45° .7071b) cos 20° .9397sin45entercos20enterNOTE: Make sure your calculator is in degree mode.
6 B. Finding angles using trig values and a calculator: Example:If 0 < < 90, what is ? Round angles to the nearest tenth.a) sin b) cos 2ndsin.5299enterYou’re “undoing” sine = 32.02ndcos.7218enter = 43.8NOTE: Make sure your calculator is in degree mode.
7 I. The Six Trigonometric Functions Cosine:cos = xSecant:sec = r=rxcos Sine:sin = yCosecant:csc = r=rysin Tangent:tan = y= sin Cotangent:cot = x= cos xcos ysin