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Sum and Difference FormulasPowerPoint Presentation

Sum and Difference Formulas

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Sum and Difference Formulas

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Sum and Difference Formulas

Dr .Hayk Melikyan

Departmen of Mathematics and CS

melikyan@nccu.edu

The cosine of the difference of two angles equals the

cosine of the first angle times the cosine of the

second angle plus the sine of the first angle times the

sine of the second angle.

Solution We know exact values for trigonometric functions of 60° and 45°. Thus, we write 15° as 60° - 45° and use the difference formula for cosines.

cos l5° = cos(60° - 45°)

= cos 60° cos 45° + sin 60° sin 45°

cos(-) = cos cos + sin sin

- Find the exact value of cos 15°

Substitute exact values from

memory or use special triangles.

Multiply.

Add.

cos(-) = cos cos + sin sin

Find the exact value of ( cos 80° cos 20° + sin 80° sin 20°) .

Solution The given expression is the right side of the formula for cos( - ) with = 80° and = 20°.

cos 80° cos 20° + sin 80° sin 20° = cos (80° - 20°) = cos 60° = 1/2

- Find the exact value of cos(180º-30º)

Solution

- Verify the following identity:

Solution

Solution

- Find the exact value of sin(30º+45º)

The tangent of the sum of two angles equals the tangent of the first angle plus the tangent of the second angle divided by 1 minus their product.

The tangent of the difference of two angles equals the tangent of the first angle

minus the tangent of the second angle divided by 1 plus their product.

Solution

- Find the exact value of tan(105º)

- tan(105º)=tan(60º+45º)

- Write the following expression as the sine, cosine, or tangent of an angle. Then find the exact value of the expression.

Solution