Note 1: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRig1dAtan03
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \arctan(-x) = {{c1::-\arctan(x)}} \] (\(\arctan\) is an {{c1::odd}} function) |
Note 2: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRig1dAtan06
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|---|---|---|
| Text | The range of \(\arctan\) is \({{c1::\left(-\frac{\pi}{2},\, \frac{\pi}{2}\right)}}\), and it is a {{c1::strictly increasing}} function. |
Note 3: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRig1dPyth01
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|---|---|---|
| Text | \[ {{c1::\sin^2\theta + \cos^2\theta :: Identity }} = {{c2::1}} \] |
Note 4: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRig1dSymm01
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \sin(-\theta) = {{c1::-\sin\theta}} \] (\(\sin\) is {{c1::odd}}) |
Note 5: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRig1dSymm02
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \cos(-\theta) = {{c1::\cos\theta}} \] (\(\cos\) is {{c1::even}}) |
Note 6: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRig1dSymm03
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \tan(-\theta) = {{c1::-\tan\theta}} \] (\(\tan\) is {{c1::odd}}) |
Note 7: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_cos_00
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \cos(0) = {{c1::1}} \] |
Note 8: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_cos_01
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \cos\!\left(\frac{\pi}{6}\right) = {{c1::\frac{\sqrt{3} }{2} }} \] |
Note 9: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_cos_02
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \cos\!\left(\frac{\pi}{4}\right) = {{c1::\frac{\sqrt{2} }{2} }} \] |
Note 10: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_cos_03
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \cos\!\left(\frac{\pi}{3}\right) = {{c1::\frac{1}{2} }} \] |
Note 11: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_cos_04
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \cos\!\left(\frac{\pi}{2}\right) = {{c1::0}} \] |
Note 12: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_cos_05
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \cos\!\left(\frac{2\pi}{3}\right) = {{c1::-\frac{1}{2} }} \] |
Note 13: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_cos_06
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \cos\!\left(\frac{3\pi}{4}\right) = {{c1::-\frac{\sqrt{2} }{2} }} \] |
Note 14: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_cos_07
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \cos\!\left(\frac{5\pi}{6}\right) = {{c1::-\frac{\sqrt{3} }{2} }} \] |
Note 15: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_cos_08
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \cos(\pi) = {{c1::-1}} \] |
Note 16: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_cos_09
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \cos\!\left(\frac{7\pi}{6}\right) = {{c1::-\frac{\sqrt{3} }{2} }} \] |
Note 17: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_cos_10
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \cos\!\left(\frac{5\pi}{4}\right) = {{c1::-\frac{\sqrt{2} }{2} }} \] |
Note 18: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_cos_11
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \cos\!\left(\frac{4\pi}{3}\right) = {{c1::-\frac{1}{2} }} \] |
Note 19: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_cos_12
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \cos\!\left(\frac{3\pi}{2}\right) = {{c1::0}} \] |
Note 20: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_cos_13
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \cos\!\left(\frac{5\pi}{3}\right) = {{c1::\frac{1}{2} }} \] |
Note 21: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_cos_14
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\[ \cos\!\left(\frac{7\pi}{4}\right) = {{c1::\frac{\sqrt{2} }{2} }} \]
Back
\[ \cos\!\left(\frac{7\pi}{4}\right) = {{c1::\frac{\sqrt{2} }{2} }} \]
Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | <br>\[ \cos\!\left(\frac{7\pi}{4}\right) = {{c1::\frac{\sqrt{2} }{2} }} \] |
Note 22: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_cos_15
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \cos\!\left(\frac{11\pi}{6}\right) = {{c1::\frac{\sqrt{3} }{2} }} \] |
Note 23: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_cos_16
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \cos(2\pi) = {{c1::1}} \] |
Note 24: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_sin_00
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \sin(0) = {{c1::0}} \] |
Note 25: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_sin_01
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \sin\!\left(\frac{\pi}{6}\right) = {{c1::\frac{1}{2} }} \] |
Note 26: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_sin_02
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \sin\!\left(\frac{\pi}{4}\right) = {{c1::\frac{\sqrt{2} }{2} }} \] |
Note 27: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_sin_03
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \sin\!\left(\frac{\pi}{3}\right) = {{c1::\frac{\sqrt{3} }{2} }} \] |
Note 28: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_sin_04
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \sin\!\left(\frac{\pi}{2}\right) = {{c1::1}} \] |
Note 29: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_sin_05
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \sin\!\left(\frac{2\pi}{3}\right) = {{c1::\frac{\sqrt{3} }{2} }} \] |
Note 30: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_sin_06
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \sin\!\left(\frac{3\pi}{4}\right) = {{c1::\frac{\sqrt{2} }{2} }} \] |
Note 31: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_sin_07
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \sin\!\left(\frac{5\pi}{6}\right) = {{c1::\frac{1}{2} }} \] |
Note 32: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_sin_08
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \sin(\pi) = {{c1::0}} \] |
Note 33: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_sin_09
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \sin\!\left(\frac{7\pi}{6}\right) = {{c1::-\frac{1}{2} }} \] |
Note 34: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_sin_10
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \sin\!\left(\frac{5\pi}{4}\right) = {{c1::-\frac{\sqrt{2} }{2} }} \] |
Note 35: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_sin_11
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \sin\!\left(\frac{4\pi}{3}\right) = {{c1::-\frac{\sqrt{3} }{2} }} \] |
Note 36: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_sin_12
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \sin\!\left(\frac{3\pi}{2}\right) = {{c1::-1}} \] |
Note 37: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_sin_13
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \sin\!\left(\frac{5\pi}{3}\right) = {{c1::-\frac{\sqrt{3} }{2} }} \] |
Note 38: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_sin_14
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \sin\!\left(\frac{7\pi}{4}\right) = {{c1::-\frac{\sqrt{2 } }{2} }} \] |
Note 39: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_sin_15
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \sin\!\left(\frac{11\pi}{6}\right) = {{c1::-\frac{1}{2} }} \] |
Note 40: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_sin_16
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \sin(2\pi) = {{c1::0}} \] |
Note 41: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_tan_00
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \tan(0) = {{c1::0}} \] |
Note 42: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_tan_01
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \tan\!\left(\frac{\pi}{6}\right) = {{c1::\frac{1}{\sqrt{3} } }} = {{c1::\frac{\sqrt{3} }{3} }} \] |
Note 43: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_tan_02
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \tan\!\left(\frac{\pi}{4}\right) = {{c1::1}} \] |
Note 44: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_tan_03
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \tan\!\left(\frac{\pi}{3}\right) = {{c1::\sqrt{3} }} \] |
Note 45: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_tan_04
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \tan\!\left(\frac{\pi}{2}\right) = {{c1::\text{undefined} }} \] |
Note 46: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_tan_05
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \tan\!\left(\frac{2\pi}{3}\right) = {{c1::-\sqrt{3} }} \] |
Note 47: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_tan_06
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \tan\!\left(\frac{3\pi}{4}\right) = {{c1::-1}} \] |
Note 48: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_tan_07
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \tan\!\left(\frac{5\pi}{6}\right) = {{c1::-\frac{\sqrt{3} }{3} }} \] |
Note 49: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_tan_08
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \tan(\pi) = {{c1::0}} \] |
Note 50: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_tan_09
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \tan\!\left(\frac{7\pi}{6}\right) = {{c1::\frac{\sqrt{3} }{3} }} \] |
Note 51: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_tan_10
Previous
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \tan\!\left(\frac{5\pi}{4}\right) = {{c1::1}} \] |
Note 52: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_tan_11
Previous
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \tan\!\left(\frac{4\pi}{3}\right) = {{c1::\sqrt{3} }} \] |
Note 53: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_tan_12
Previous
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \tan\!\left(\frac{3\pi}{2}\right) = {{c1::\text{undefined} }} \] |
Note 54: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_tan_13
Previous
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \tan\!\left(\frac{5\pi}{3}\right) = {{c1::-\sqrt{3} }} \] |
Note 55: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_tan_14
Previous
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \tan\!\left(\frac{7\pi}{4}\right) = {{c1::-1}} \] |
Note 56: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_tan_15
Previous
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \tan\!\left(\frac{11\pi}{6}\right) = {{c1::-\frac{\sqrt{3} }{3} }} \] |
Note 57: ETH::2. Semester::Analysis
Note Type: Horvath Cloze
GUID:
tRigUC_tan_16
Previous
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Field-by-field Comparison
| Field | Before | After |
|---|---|---|
| Text | \[ \tan(2\pi) = {{c1::0}} \] |