MAC 1114 2/2/16 notes
MAC 1114 2/2/16 notes MAC 1114
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This 8 page Class Notes was uploaded by Heya_Lanayia on Tuesday February 9, 2016. The Class Notes belongs to MAC 1114 at Florida State University taught by Dr. LeNoir in Winter 2016. Since its upload, it has received 105 views. For similar materials see Analytic Trigonometry MAC1114 in Math at Florida State University.
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Date Created: 02/09/16
MAC 1114 Analytic Trigonometry 2/2/16 notes 8. Rewrite an equivalent expression (HINT: use reference angles) 2 a) tan (7pi/9) Step 1: Draw/ locate angle Step 2: Determine if trig ratio is negative or positive In this case tan is going to be negative, because 7pi/9 falls in quadrant 2, where only Sin is positive. Step 3: Find reference angle The reference angle is the distance between the terminal angle, and the nearest x axis. To find the reference angle in this case you’d just do 9pi/9 – 7pi/9, which equals 2pi/9, so 2pi/9 is the reference angle. Step 4: Put it all together So final answer: tan (7pi/9)= tan (2pi/9) ***tan becomes (+)tan because of it’s squared, and a negative times a negative is always a positive. Remember that this only works if the trig ratios are the SAME, and if you use the REFERENCE angle. b) csc (15pi/11) ****The pi next to 11pi/11 should be positive. Somehow the negative sign got cut off. Sorry guys! csci the reciprocal of sine, therefore csc is also positive by being in the second quadrant. The reference angle is 4pi/11 (15pi/11 11pi/11) ***reference angles are always positive!!*** Final answer: csc (15pi/11)= csc (4pi/11) 2 c) sin (4pi/7) The angle is in the 3 quadrant, so it’s negative (because only tan is positive in quadrant 3, and we’re dealing with sin). The reference angle is 3pi/7. 2 2 Final answer: si (4pi/7)=sin (3pi/7) 2 It should –sin (3pi/7), but as we did earlier, a negative times a negative is a positive. 9. Rewrite equivalent expressions (HINT: use confunctions of complimentary angles) a) cos (7pi/18) We’re gonna use similar steps as earlier. We’re gonna draw/ locate angle, determine if the ratio is positive or negative, find the complimentary angle (2 angles that add to pi/2), and then put it all together So we end up with ***This works because COsine and sin are COfunctions, and 7pi/18 and pi/9 are complimentary angles ***Tan and COtangent are also COfunctions *** Secant and COsecant are also COfunctions Final answer: cos (7pi/18)= sin (pi/9) 2 9b. cot (11pi/16) **For this one we have to use reference angles, and complimentary/ confunctions 2 2 2 Final answer: cot (11pi/16)= cot (5pi/16)=tan (3pi/16) You can go from the first to second ratio because 5pi/16 is the reference angle of 11pi/16. You can go from the second to third ratio because 5i/16 and 3pi/16 are complimentary angles, and tan AND cot are cofunctions 2 2 2 11. cot (8pi/3)sin (2pi/9)sin (5pi/18) The graphics aren’t the best, but let me know what you’re having trouble reading and I’ll get back to you asap Reflections
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