Trigonometric Functions Chapter 6 Trigonometric Functions

Section 2 Trigonometric Functions: Unit Circle Approach

Review: The unit circle is made up of a bunch of right triangles The radius of the unit circle = 1

Review of right triangle trig Unknown angle measures = 𝜃, 𝛼, 𝛽 (Greek letters) theta, lambda, beta General Trig Functions Unit Circle Trig sin 𝜃 = opp/hyp sin 𝜃 = y cos 𝜃 = adj/hyp cos 𝜃 = x tan 𝜃 = opp/adj = sin 𝜃/cos 𝜃 tan 𝜃 = y/x csc 𝜃 = hyp/opp = 1/sin 𝜃 csc 𝜃 = 1/y sec 𝜃 = hyp/adj = 1/cos 𝜃 sec 𝜃 = 1/x cot 𝜃 = adj/opp = cos 𝜃/sin 𝜃 = 1/tan 𝜃 cot 𝜃 = x/y ** 1/something = take reciprocal

Example: If the point P is on the unit circle and represents the angle t and P = (-2/5, 2 2 5 ), find all 6 trig functions of t. **since they said P was on the unit circle, use unit circle trig** sin t cos t tan t csc t sec t cot t

Example: If the point (2, -3) is on the terminal side of 𝜃 in standard position find all six trig function. **not on unit circle so use the point to create a triangle and use standard trig functions** sin 𝜃 cos 𝜃 tan 𝜃 csc 𝜃 sec 𝜃 cot 𝜃

Example: Find the exact values of the following: sin 3𝜋 cos (-270*)

Example: Find the exact values: sin 45. cos 180 Example: Find the exact values: sin 45* cos 180* tan(𝜋/4) – sin(3𝜋/2) (sec (𝜋/4))2 + csc(𝜋/2)

Example: Find the exact value: 4 sin 90* - 3 tan 180*

EXIT SLIP