0709 ch 7 day 9

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  • 0709 ch 7 day 9

    1. 1. 7.4 Inverse Trig Functions Day 2Psalm 46:1God is our refuge and strength, an ever-present help in trouble.
    2. 2. Groups: Simplify (find the exact values): ⎛ 2 ⎞ −1 1. sin ⎜ ⎝ 2 ⎟ ⎠ ⎛ −1 3 ⎞ 2. cos ⎜ − ⎝ 2 ⎟ ⎠ 3. tan −1 3 −1 4. tan − 3
    3. 3. Groups: Simplify (find the exact values): ⎛ 2 ⎞ −1 π 1. sin ⎜ 1. ⎝ 2 ⎟ ⎠ 4 ⎛−1 3 ⎞ 5π 2. cos ⎜ − 2. ⎝ 2 ⎟ ⎠ 6 −1 π 3. tan 3 3. 3 −1 π 4. tan − 3 4. − 3
    4. 4. Groups: Simplify (find the exact values): ⎛ 2 ⎞ −1 π 1. sin ⎜ 1. ⎝ 2 ⎟ ⎠ 4 ⎛−1 3 ⎞ 5π 2. cos ⎜ − 2. ⎝ 2 ⎟ ⎠ 6 −1 π 3. tan 3 3. 3 −1 π 4. tan − 3 4. − 3 5π to answer #4 as would be wrong because 3 ⎡ π π ⎤ tan x has a range of −1 ⎢ − 2 , 2 ⎥ ⎣ ⎦
    5. 5. Let’s go through this one together: ⎛ −1 ⎛ 1 ⎞ ⎞ 5. tan ⎜ sin ⎜ ⎟ ⎟ ⎝ ⎝ 5 ⎠ ⎠
    6. 6. Let’s go through this one together: ⎛ −1 ⎛ 1 ⎞ ⎞ 5. tan ⎜ sin ⎜ ⎟ ⎟ ⎝ ⎝ 5 ⎠ ⎠ sin −1 x is + in QI
    7. 7. Let’s go through this one together: ⎛ −1 ⎛ 1 ⎞ ⎞ 5. tan ⎜ sin ⎜ ⎟ ⎟ ⎝ ⎝ 5 ⎠ ⎠ sin −1 x is + in QI 5 1 θ a
    8. 8. Let’s go through this one together: ⎛ −1 ⎛ 1 ⎞ ⎞ 5. tan ⎜ sin ⎜ ⎟ ⎟ ⎝ ⎝ 5 ⎠ ⎠ sin −1 x is + in QI 2 2 2 a +1 = 5 5 2 1 a = 24 θ a=2 6 a
    9. 9. Let’s go through this one together: ⎛ −1 ⎛ 1 ⎞ ⎞ 5. tan ⎜ sin ⎜ ⎟ ⎟ ⎝ ⎝ 5 ⎠ ⎠ sin −1 x is + in QI 2 2 2 a +1 = 5 5 2 1 a = 24 θ a=2 6 a 1 tan θ = 2 6
    10. 10. Let’s go through this one together: ⎛ −1 ⎛ 1 ⎞ ⎞ 5. tan ⎜ sin ⎜ ⎟ ⎟ ⎝ ⎝ 5 ⎠ ⎠ sin −1 x is + in QI 2 2 2 a +1 = 5 5 2 1 a = 24 θ a=2 6 a 1 tan θ = 2 6 1 6 = g 2 6 6
    11. 11. Let’s go through this one together: ⎛ −1 ⎛ 1 ⎞ ⎞ 5. tan ⎜ sin ⎜ ⎟ ⎟ ⎝ ⎝ 5 ⎠ ⎠ sin −1 x is + in QI 2 2 2 a +1 = 5 5 2 1 a = 24 θ a=2 6 a 1 tan θ = 2 6 1 6 = g 2 6 6 6 = 12
    12. 12. ⎛ −1 ⎛ 3 ⎞ ⎞Groups: 6. cos ⎜ tan ⎜ ⎟ ⎟ ⎝ ⎝ 8 ⎠ ⎠
    13. 13. ⎛ −1 ⎛ 3 ⎞ ⎞Groups: 6. cos ⎜ tan ⎜ ⎟ ⎟ ⎝ ⎝ 8 ⎠ ⎠ c 2 2 3 +8 =c 2 3 θ c = 73 8
    14. 14. ⎛ −1 ⎛ 3 ⎞ ⎞Groups: 6. cos ⎜ tan ⎜ ⎟ ⎟ ⎝ ⎝ 8 ⎠ ⎠ c 2 2 3 +8 =c 2 3 θ c = 73 8 8 cosθ = 73 8 73 = 73
    15. 15. ⎛ ⎛ 87π ⎞ ⎞Together: −1 7. sin ⎜ sin ⎜ ⎟ ⎟ ⎝ ⎝ 4 ⎠ ⎠
    16. 16. ⎛ ⎛ 87π ⎞ ⎞Together: −1 7. sin ⎜ sin ⎜ ⎟ ⎟ ⎝ ⎝ 4 ⎠ ⎠ 87π 7π 1st wrap equivalent of is 4 4
    17. 17. ⎛ ⎛ 87π ⎞ ⎞Together: −1 7. sin ⎜ sin ⎜ ⎟ ⎟ ⎝ ⎝ 4 ⎠ ⎠ 87π 7π 1st wrap equivalent of is 4 4 ⎛ 7π ⎞ −1 ∴ = sin ⎜ sin ⎟ ⎝ 4 ⎠
    18. 18. ⎛ ⎛ 87π ⎞ ⎞Together: −1 7. sin ⎜ sin ⎜ ⎟ ⎟ ⎝ ⎝ 4 ⎠ ⎠ 87π 7π 1st wrap equivalent of is 4 4 ⎛ 7π ⎞ −1 ∴ = sin ⎜ sin ⎟ ⎝ 4 ⎠ −1 ⎡ π π ⎤ since sin is defined from ⎢ − 2 , 2 ⎥ ⎣ ⎦
    19. 19. ⎛ ⎛ 87π ⎞ ⎞Together: −1 7. sin ⎜ sin ⎜ ⎟ ⎟ ⎝ ⎝ 4 ⎠ ⎠ 87π 7π 1st wrap equivalent of is 4 4 ⎛ 7π ⎞ −1 ∴ = sin ⎜ sin ⎟ ⎝ 4 ⎠ −1 ⎡ π π ⎤ since sin is defined from ⎢ − 2 , 2 ⎥ ⎣ ⎦ 7π π is incorrect ... but − is correct! 4 4
    20. 20. Together: Find approximate first wrap angles.
    21. 21. Together: Find approximate first wrap angles. ⎛ 6 ⎞ −1 8. sin ⎜ ⎟ (in radians) ⎝ 7 ⎠
    22. 22. Together: Find approximate first wrap angles. ⎛ 6 ⎞ −1 8. sin ⎜ ⎟ (in radians) ⎝ 7 ⎠ 1.0297
    23. 23. Together: Find approximate first wrap angles. ⎛ 6 ⎞ −1 8. sin ⎜ ⎟ (in radians) ⎝ 7 ⎠ 1.0297 9. tan −1 ( −15 )
    24. 24. Together: Find approximate first wrap angles. ⎛ 6 ⎞ −1 8. sin ⎜ ⎟ (in radians) ⎝ 7 ⎠ 1.0297 9. tan −1 ( −15 ) Calculator gives us -1.5042, but this is not in the first wrap. Add 2π
    25. 25. Together: Find approximate first wrap angles. ⎛ 6 ⎞ −1 8. sin ⎜ ⎟ (in radians) ⎝ 7 ⎠ 1.0297 9. tan −1 ( −15 ) Calculator gives us -1.5042, but this is not in the first wrap. Add 2π 4.7790 If the directions didn’t ask for the first wrap ... -1.5042 would be fine.
    26. 26. HW #7To avoid situations in which you might make mistakesmay be the biggest mistake of all. Peter McWilliams

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