Pillow English Listening

• Even/Odd Identities
Even/Odd Identities SOH CAH TOA sin(-x) = -sin(x)︱cos(-x) = cos(x)︱tan(-x) = -tan(x) csc(-x) = -csc(x)︱sec(-x) = sec(x)︱cot(-x) = -cot(x) Slope is rise over run. ⦶(-x) = -⦶(x)︱⊖(-x) = ⊖(x)︱⊘(-x) = -⊘(x) ⦶⁻¹(-x) = -⦶⁻¹(x)︱⊖⁻¹(-x) = ⊖⁻¹(x)︱⊘⁻¹(-x) = -⊘⁻ ...
3677#5011 SBLNGS CHLDRN 5011

○○○ Even/Odd Identities ⪢⪢
3677#5014 SBLNGS CHLDRN 5014

• Periodic Identities
Periodic Identities SOH CAH TOA sin(x+2nπ) = sin(x) cos(x+2nπ) = cos(x) tan(x+nπ) = tan(x) csc(x+2nπ) = csc(x) sec(x+2nπ) = sec(x) cot(x+nπ) = cot(x) Slope is rise over run and 1 turn is 2π radians. ⦶(x+n) = ⦶(x) ⊖(x+n) = ⊖(x) ⊘(x+n/2) = ⊘(x) ⦶⁻¹(x+n) ...
3677#5015 SBLNGS CHLDRN 5015

○○○ Periodic Identities ⪢⪢
3677#3463 SBLNGS CHLDRN 3463

• Pythagorean Identities
Pythagorean Identities SOH CAH TOA sin²(x) + cos²(x) = 1 tan²(x) + 1 = sec²(x) 1 + cot²(x) = csc²(x) Slope is rise over run. ⦶²(x) + ⊖²(x) = (opposite/hypotenuse)² + (adjacent/hypotenuse)² = hypotenuse²/hypotenuse² = 1 ⊘²(x) + 1 = ⊖⁻²(x) 1 + ⊘⁻²(x) = ...
3677#9674 SBLNGS CHLDRN 9674

○○○ Pythagorean Identities ⪢⪢
3677#5010 SBLNGS CHLDRN 5010

• Sums and Differences Identities Derivation
Sums and Differences Identities Derivation Suppose two points with coordinates of (⊖α,⦶α) and (⊖β,⦶β). Then the distance between the two points is √( (⊖α - ⊖β)² + (⦶α - ⦶β)² ). It is the same as the distance between (⊖(α-β), ⦶(α-β)) and (1,0), which is ...
3677#5021 SBLNGS CHLDRN 5021

○○○ Sums and Differences Identities Derivation ⪢⪢
3677#5022 SBLNGS CHLDRN 5022

• Tangent and Reciprocal Identities
Tangent Identities SOH CAH TOA tan(x) = sin(x)/cos(x) cot(x) = cos(x)/sin(x) Slope is rise over run. ⊘(x) = ⦶(x)/⊖(x)︱⊘⁻¹(x) = ⊖(x)/⦶(x) Reciprocal Identities SOH CAH TOA csc(x) = 1/sin(x) sec(x) = 1/cos(x) cot(x) = 1/tan(x) Slope is rise over run. ...
3677#5006 SBLNGS CHLDRN 5006

○○○ Tangent and Reciprocal Identities ⪢⪢
3677#5007 SBLNGS CHLDRN 5007