Lab 6.5 Trigonometric Equations PDF

Lab 6.5 Trigonometric Equations Solve the following equation. Give all solutions in radians and within the interval [0, 2π). 2 1. 2𝑐𝑜𝑠 𝑥 + 𝑠𝑖𝑛 𝑥 − 1 = 0 2. 𝑠𝑖𝑛 (2𝑥) = 𝑐𝑜𝑠 𝑥 3. (𝑡𝑎𝑛 𝑥 − 1)(𝑐𝑜𝑠 𝑥 − 1) = 0 4. (2𝑐𝑜𝑠 𝑥 − 3 )(2𝑠𝑖𝑛 𝑥 − 1) = 0 5. 𝑐𝑜𝑠 (2𝑥) = 𝑐𝑜𝑠 𝑥...

Lab 6.5 Trigonometric Equations Solve the following equation. Give all solutions in radians and within the interval [0, 2π). 2 1. 2𝑐𝑜𝑠 𝑥 + 𝑠𝑖𝑛 𝑥 − 1 = 0 2. 𝑠𝑖𝑛 (2𝑥) = 𝑐𝑜𝑠 𝑥 3. (𝑡𝑎𝑛 𝑥 − 1)(𝑐𝑜𝑠 𝑥 − 1) = 0 4. (2𝑐𝑜𝑠 𝑥 − 3 )(2𝑠𝑖𝑛 𝑥 − 1) = 0 5. 𝑐𝑜𝑠 (2𝑥) = 𝑐𝑜𝑠 𝑥 2 6. 4𝑠𝑖𝑛 𝑥 + 4𝑐𝑜𝑠 𝑥 − 5 = 0 2 7. 2𝑡𝑎𝑛 𝑥 + 5𝑡𝑎𝑛 𝑥 + 3 = 0 8. 𝑐𝑜𝑠 𝑥 − 5 = 3𝑐𝑜𝑠 𝑥 + 6 Solve the following equation using a calculator. Give all the solutions in radians rounded to 2 decimal places and within the interval [ 0, 2𝜋 ) 9. 𝑠𝑖𝑛 𝑥 = 0. 8246 10. 𝑐𝑜𝑠 𝑥 =− 0. 4721 11. 𝑠𝑖𝑛 𝑥 = 1. 1414 12. 𝑡𝑎𝑛 𝑥 =− 1. 1285 Simplify into a single Trig Function 𝑐𝑜𝑠 (𝑥) 𝑠𝑒𝑐 (𝑥) 13. 𝑡𝑎𝑛 (𝑥) 𝑡𝑎𝑛 (𝑥) − 𝑐𝑜𝑡 (−𝑥) 14. 𝑠𝑒𝑐 (𝑥) 2 (𝑠𝑖𝑛 𝑥 + 𝑐𝑜𝑠 𝑥) −1 15. 2 𝑐𝑜𝑠 𝑥 1 16. (𝑡𝑎𝑛 𝑦 + 𝑐𝑜𝑡 𝑦)𝑠𝑖𝑛 𝑦 𝑐𝑠𝑐 𝑥 − 𝑐𝑜𝑡 𝑥 17. 𝑠𝑒𝑐 𝑥 −1 𝑐𝑜𝑠 𝑥 18. 1−𝑠𝑖𝑛 𝑥 + tan (−x) Use a double-angle or half-angle identity to find the exact value of each expression. 7 θ 19. 𝑠𝑖𝑛 θ = − and 270° < θ < 360°. Find 𝑐𝑜𝑠 25 2 4 20. 𝑐𝑜𝑠 θ = and 270° < θ < 360°. Find 𝑠𝑖𝑛 2θ 5 3 3π θ 21. 𝑠𝑖𝑛 θ = − and < θ < 2π. Find 𝑡𝑎𝑛 5 2 2 3 91 3π 22. 𝑐𝑜𝑡 θ = − and < θ < 2π. Find 𝑡𝑎𝑛 2θ 91 2 13 π 23. 𝑠𝑒𝑐 θ = − 5 and 2 < θ < π. Find 𝑐𝑜𝑠 2θ Use a sum and difference identity to find the exact value of each expression. 24. 𝑠𝑖𝑛 (− 15°) 25. 𝑐𝑜𝑠 (− 105°) 5π 26. 𝑡𝑎𝑛 12 π 2π π 2π 27. 𝑠𝑖𝑛 9 𝑐𝑜𝑠 9 + 𝑐𝑜𝑠 9 𝑠𝑖𝑛 9 𝑡𝑎𝑛 76° + 𝑡𝑎𝑛 164° 28. 1 − 𝑡𝑎𝑛 76° 𝑡𝑎𝑛 164°