Solve the following trigonometric equations. · cos(x) = } · cos(x) + V3 sin(x) = V2
9. Write the given expression as a sin 2x 1-cos 2x single trigonometric function 10. Solve for x. 2cos'x-cos x 1
9. Write the given expression as a sin 2x 1-cos 2x single trigonometric function 10. Solve for x. 2cos'x-cos x 1
More Trigonometric Equations to use for Pass the Pen Learning objectives: After this activity, you should be comfortable with solving trigonometric equations with no period adjustment. Solve the following equations for in (0,25) 1. V3 sin(8) = 2 2. cos(@) sin(O) = 0 3. cost = cost
Solve the following equations for x if 0° < 0 < 360°. 36. 2 cos 20 + sin 0 = 1 35. 1 - 4 cos 0 = -2 cos2 37. sin (30 – 45) = -V3 38. cos 30 = -2
2. Solve the given trigonometric equation using Pythagorian Identities, cos? 0 + sin? 0 = 1, 1+tan? 0 = sec, cot? 0+1 = csc 0. (a) 1 - 2 sin’x = cos r. (b) 4 sin’t - 5 sin x - 2 cos” x = 2. (c) 2 tang - 2 sec1+1= = tan”.
O TRIGONOMETRIC IDENTITIES AND EQUATIONS Double-angle identities: Problem type 1 3 Find sin 2x, cos 2x, and tan 2x if sinx and x terminates in quadrant III. 10 . 0/0 sin 2x = X5 ? cos 2x tan 2x L
cos 2x </ 0.8x-1.9
= O TRIGONOMETRIC IDENTITIES AND EQUATIONS Using a graphing calculator to solve a trigonometric inequality Use the ALEKS graphing calculator to solve the inequality cos2x<0.8x-1.9 with x in radians. Write your answer using interval notation, with values rounded to 2 de (0,0) [0,0] (0,0) (0,0) DUO -00 8. X 5 ?
14. Prove the trigonometric identity: (4) 2) (sin x + cos x)() come an d sin 2x – cas e
1-2 cose Solve the following trigonometric identity: cos sin e tan 8 – cote. Show all your steps for full marks. [4T]
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Problem 4: Assume Vin 10 cos(201) 4a) Write the voltage node equations for the following circuit. 4b) Solve for V1, V2, and V3 4c) Simulate this circuit in PartSim and check your answers VO 10 V1 20 V2 V3 1mF 2mF 3mF Vin(ヘン Problem4
Problem 4: Assume Vin 10 cos(201) 4a) Write the voltage node equations for the following circuit. 4b) Solve for V1, V2, and V3 4c) Simulate this circuit in PartSim and check your answers...
need help wirh all three
5. Solve the equations: (a) cos(x + 1) - cos x – 1= 0 (b) cos 2x – cos 6x = 0 (c) sin 2x sin x = cos x