5.1 - Trig Functions of Any Angle Notes Key Day

Honors Algebra 2 5.1 ‐ Trigonometric Functions of Any Angle Do‐Now: Fill in the definitions for the six trig functions given the image below. sin (θ) = _____ csc (θ) = _____ cos (θ) = _____ sec (θ) = _____ tan (θ) = _____ cot (θ) = _____ **These functions are also referred to as circular functions.** Examples: 1. Use the given point on the terminal side of an angle θ in standard position. Evaluate the six trig. functions of θ. (Notice the signs of the points) a.) b.) c.) What if the angle's terminal side falls on the x or y axis when it is in standard position? Well, that's called a ________________ ____________. What are some examples of quadrantal angles? 2. Evaluate the six trig. functions for θ = ‐270o . 1 Honors Algebra 2 Now, let's think about the Unit Circle again! What was special about the unit circle? (Hint: Every triangle that made it up had one thing in common.) So, our conclusion was that (x , y) ‐‐‐> ( __________ , __________ ) 3. Use the unit circle to evaluate the six trig. functions for the given value of θ. a. 180o b. (3π/2) c. ‐ 315o d. (4π/3) 2 Honors Algebra 2 Think: Use the relationships that we just talked about to help label the signs for each of the 6 trig. functions in each quadrant. Reference Angles ‐ Examples: Find the reference angle for each θ given. 1. θ = 300o 2. θ = ‐ 210o 3. θ = (5π/4) 4. θ = ‐(4π/3) 5. θ = ‐(5π/6) 6. θ = (11π/6) 3 Honors Algebra 2 To Evaluate Trigonometric Functions for Any Angle: 1. Find the reference angle. 2. Evaluate the trig function for the reference angle. 3. Change the sign of the trig. function as needed. (Refer to the chart that we made for the Do‐Now) Evaluate each function without using a calculator. You can draw the right triangle that is formed by the angle, as a reference if needed. 7. cos ( ‐ 225o) 8. tan (330o) 9. sin ( ‐ (5π/3)) 10. sec (5π/4) 11. cot (4π/3) 12. csc (225o) 4