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9.2 - Sum and Difference Identities Proof of the Difference Formula for Cosines We can find the distance from P to Q using the distance formula. Lecture notes developed under creative commons license using OpenStax Algebra and Trigonometry, Algebra and Trigonometry. OpenStax CNX. May 18, 2016 http://cnx.org/contents/[email protected] Point P is at an angle α from the positive x- axis with coordinates (cosα, sinα) and point Q is at an angle of β from the positive x-axis with coordinates(cosβ,sinβ).Note the measure of angle POQ is α−β. Label two more points: A at an angle of (α−β) from the positive x-axis with coordinates(cos(α−β), sin(α−β)); and point B (1,0). POQ
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9.2 - Sum and Difference IdentitiesProof of the Difference Formula for Cosines
We can find the distance from P to Q using the distance formula.
Lecture notes developed under creative commons license using OpenStax Algebra and Trigonometry, Algebra and Trigonometry. OpenStax CNX. May 18, 2016 http://cnx.org/contents/[email protected]
Point P is at an angle α from the positive x-axis with coordinates (cosα, sinα) and point Q is at an angle of β from the positive x-axis with coordinates(cosβ,sinβ).Note the measure of angle POQ is α−β.
Label two more points: A at an angle of (α−β) from the positive x-axis with coordinates(cos(α−β), sin(α−β)); and point B with coordinates(1,0).Triangle POQ is a rotation of triangle AOB and thus the distance from P to Q is the same as the distance from A to B.
Example
Lecture notes developed under creative commons license using OpenStax Algebra and Trigonometry, Algebra and Trigonometry. OpenStax CNX. May 18, 2016 http://cnx.org/contents/[email protected]
Using the Sum and Difference Formulas for Sine
Examples
Lecture notes developed under creative commons license using OpenStax Algebra and Trigonometry, Algebra and Trigonometry. OpenStax CNX. May 18, 2016 http://cnx.org/contents/[email protected]
Using the Sum and Difference Formulas for Tangent
Examples
Lecture notes developed under creative commons license using OpenStax Algebra and Trigonometry, Algebra and Trigonometry. OpenStax CNX. May 18, 2016 http://cnx.org/contents/[email protected]
Using the Sum and Difference Formulas for Cofunctions
Lecture notes developed under creative commons license using OpenStax Algebra and Trigonometry, Algebra and Trigonometry. OpenStax CNX. May 18, 2016 http://cnx.org/contents/[email protected]
Examples
Using the Sum and Difference Formulas to Verify Identities
Example
Lecture notes developed under creative commons license using OpenStax Algebra and Trigonometry, Algebra and Trigonometry. OpenStax CNX. May 18, 2016 http://cnx.org/contents/[email protected]
Lecture notes developed under creative commons license using OpenStax Algebra and Trigonometry, Algebra and Trigonometry. OpenStax CNX. May 18, 2016 http://cnx.org/contents/[email protected]
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