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  1. 1Sine of 7π/6
  2. 2Secant of 2π/3
  3. 3Cosine of 3π/4
  4. 4Degrees to radians
  5. 5Radians to degrees
  6. 6Arc length from radians
  7. 8Double angle from sinθ
  8. 10Solving 2sinx−1=0
  9. 12Solving tanx=√3
  10. 14Law of sines for a side
  11. 15Law of cosines, finding a side
  12. 17Area with two sides and angle
  13. 19Inverse sine and cosine angles
  14. 20Evaluating log expressions
  15. 21Logs: solving log equation
  16. 22Solving ln(2x+1)=3
  17. 24Solving exponential growth
  18. 25Solving a cubic by factoring
  19. 26Remainder theorem
  20. 28Asymptotes of a rational function
  21. 30Arithmetic sequence term and sum
  22. 31Geometric sequence, 8th term and sum
  23. 33Vector magnitude and dot product
  24. 35Resolving a force vector
  25. 36Multiplying complex numbers

8Double angle from sinθ

sin θ = 5/13 and θ is acute. Find sin 2θ and cos 2θ.

sin2θ = 120/169 and cos2θ = 119/169. First get cosθ = 12/13 from the right triangle (5-12-13), then use sin2θ = 2sinθcosθ and cos2θ = cos²θ − sin²θ. Check: (120/169)² + (119/169)² = 1.

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