generate new values of X ~ f(x) = sin(x) (sin (x, + 0.00 *1 0.0 -7 0.75423062 -6.9 0.81601418 -6.8 0.8696444 -6.7 0.91458542 -6.6 0.9503882 Derivative of sin(x) Insert / attach a screenshot of both plots along with the table of values. What can you say about the graph of the derivative of sin (x)? What does it look like? Derivative of cos (x) Repeat steps 2-6 for f(x) = cos(x) Insert / attach a screenshot of both plots along with the table of values. What can you say about the graph of the derivative of cos(x)? What does it look like? Additional Review of Trig Functions 1. Start with f (x) = sin(x) 2. Change the x-axis settings so that it divides the x-axis (gridlines) as a fraction of It. Adjust the y-axis as needed. Display Reverse Contrast Braille Mode Grid Axis Numbers Minor Gridlines Arrows Zoom Square -2TT -3TT/2 -TT/2 X-Axis add a label -271 S XS 2x Step: 5 VY-Axis add a label -2 Sys2 Step Lock Viewport 3. Modify the function to f (x) = A sin(x) and add a slider for A. Move the slider and observe its effect on the graph. 4. Modify the function to f (x) = A sin(x - d) and add a slider for d. Move the shi serve its effect onA5.4 Derivative of Trig Functions - I10 Goal: 0 Use table of values to numerically determine the derivative of f(x) = 5in(x) and f(x) = 6050:) Recall: . _ - Lt). f (x) _ lll'l'l x+hh x h ) 0 We can approximate it by using very small values of h: f'(x) z fix+hh!xi When f(x) = sin(x) . "(+h ' f (x) z smx 21 sm(x) Instructions 1. Open desmos. Plot the following functions and then review their graphs: sin(x), cos(x), tan(x). 2. Clear all graphs and inputjust the sine function f(x) = sin(x) sin(x1+0.001) sin(x1) 3. Add a table and replace yl with 0 001 + r f(.\\') expression \"'1 note 4. Enter the rst value for x1 (e.g. -6.28) and then enter the next value (e.g. -6.1B). The approximate value for the slope of the tangent will be computed automatically. Keep pressing enter to automatically generate new values of 961 a m) =sm(x) 9 (sin(x, + 00 x1 _ uerlvative OT CU.) {1'} Repeat steps 2-6 for f(x) = cos(x) Insert/attach a screenshot of both plots along with the table of values. What can you say about the graph of the derivative of cos(x)? What does it look like? 4of4 Additional Review of Trig Functions 1. Start with f (x) = sin(x) 2. Change the x-axis settings so that it divides the xaxis (gridlines) as a fraction of TI. Adjust the yaxis as needed. 2 Display . l7 Reverse Contrast l7 Braille Mode i? Gun VANS Numbers . V MIVIW Gmlines ZMnSw-r: l Arrows l" W5 l; 7M 51521 eten' ' 7 .mmus [7.4mm l .2 gygz Stan i LockVieprl o 3. Modify the function to f(x) = A Sin(x) and add a slider for A. Move the slider and observe its effect on the graph. 4. Modify the function to f(x) = A sin(x d) and add a slider for d. Move the slider to change the value of and observe its effect on the graph. (Note you can change the step amount for d to be a multiple/fraction of TE). 5. Modify the function to f(x) = A sin(x d) + C and adda slider for 6. Move the slider to change the value of and observe its effect on the graph. 6. Modify the function to f(x) = A Sin (k(x d)) + C and add a slider for k. Move the slider to change the value of k and observe its effect on the graph. (Initially, keep (1 = 0 and C = 0 as you change the value of k.) 7. Observe / note down the following for each Trig function: - Asin (k(x (1)) + C Acos(k(x d)) + c Range Amplitude Period Horizontal Shift