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Sum and difference formulas Sum and difference formulas

Sum and difference formulas - PowerPoint Presentation

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Uploaded On 2017-09-05

Sum and difference formulas - PPT Presentation

Onward to Section 53 Well start with two diagrams What is the relationship between the three angles What is the relationship between the two chords Distance formula Square both sides and expand the binomials ID: 585394

difference sum formula identity sum difference identity formula expression sinusoid find exact sine practice algebraically tangent thegiven guided verifying

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Slide1

Sum and difference formulas

Onward to Section

5.3Slide2

We’ll start with two diagrams:

What is the relationship between the three angles?

What is the relationship between the two chords?

Distance formula:Slide3

Square both sides and expand the binomials:Slide4

(Note the sign switch in either case.)

Cosine of a Sum or DifferenceSlide5

What about the sine of a sum or difference?

Start with a

cofunction

identity:

Our new identity!!!Slide6

(Note that the sign does not switch in either case.)

Sine of a Sum or DifferenceSlide7

Directly from our previous two identities:

Tangent of a Sum or Difference

Or, use a new formula that is written entirely in terms of tangent:Slide8

Use a sum or difference identity to find an exact value of thegiven expression.

Guided Practice

1.

Any other way to simplify

this expression?

Any way to check our work

with a calculator?Slide9

Use a sum or difference identity to find an exact value of thegiven expression.

Guided Practice

2.Slide10

Use a sum or difference identity to find an exact value of thegiven expression.

Guided Practice

3.Slide11

Use a sum or difference identity to find an exact value of thegiven expression.

Guided Practice

4.Slide12

Use a sum or difference identity to find an exact value of thegiven expression.

Guided Practice

5.Slide13

Some problems require us to simply recognize certain trig.

identities…

Write the given expressions as the sine, cosine, or tangent of an

angle.

This is the sine of a sum formula!!!

This is the cosine of a

difference formula!!!Slide14

Some problems require us to simply recognize certain trig.

identities…

Write the given expressions as the sine, cosine, or tangent of an

angle.

This is the

opposite

of the

cosine of a sum formula!!!

This is the tangent of a

difference formula!!!Slide15

Verifying a Sinusoid Algebraically

Previously, we were able to re-write expressions like

as

Now, we will find an

exact

value for this function…

In general, using the sine of a sum formula:

Here, we have:

Compare coefficients:Slide16

Verifying a Sinusoid Algebraically

Solve for

a

algebraically:

Choosing

a

to be

positive gives us:

Final Answer:

orSlide17

Verifying a Sinusoid Algebraically

Express the function as a sinusoid in the form

Compare coefficients:

Solve for

a

:

Verify graphically?Slide18

Verifying a Sinusoid Algebraically

Express the function as a sinusoid in the form

Compare coefficients:

Solve for

a

:

Verify graphically?