Find the measure(s) of given the value of the trig function:1) 2)

Warm - Up

Trigonometric IdentitiesSection 5.1

ObjectivesStudents will be able to…•

Unit Time Line• Friday (5/15)– Basic Trig Identities (Sect. 5.1)• Monday – Thursday (5/18 – 12/21) – Verifying Trig Identities (Sect. 5.2)• Friday (5/22) – Review/Practice• Tuesday (5/26) – Quest (Sects. 5.1 – 5.2)• Wednesday, Thursday (5/27 – 5/28) – Solving Trig Identities (Sect. 5.3)• Friday (5/29) – Practice/Core Assessment• Monday (6/1) – Review• Tuesday (6/2) – Quest (Sect. 5.3)

Trigonometric IdentityDefinition: a statement of equality between 2 expressions that is true for all valuesTrig Notation:

YOU ARE EXPECTED TO KNOW ALL OF THE FOLLOWING FUNDAMENTAL IDENTITIES FROM MEMORY!!

Reciprocal Identitiessin 𝑥=

1csc 𝑥

csc 𝑥=1sin 𝑥 sin 𝑥⋅csc 𝑥=1

cos𝑥=1sec𝑥

sec𝑥=1

cos𝑥 cos𝑥 ⋅sec 𝑥=1

tan𝑥=1cot 𝑥

cot 𝑥=1tan𝑥 tan𝑥 ⋅cot 𝑥=1

Quotient Identities

tan𝑥=sin 𝑥cos𝑥

cot 𝑥=cos𝑥sin 𝑥

Recall the unit circle…

Pythagorean Theorem…Substitution …

Pythagorean Identities(x, y)… (________, ________)

Case 1: Using given values of trig functions to find other trig functions

Use the values and to calculate the values of all six trig functions

Case 1: Using given values of trig functions to find other trig functions

Use the values and to calculate the values of all six trig functions

Case 2: Simplifying a Trigonometric Expression

Statement Reason

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Case 2: Simplifying a Trigonometric Expression

Statement Reason

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Examples:

Case 3: Review of Factoring Techniques

sin 𝑥1+cos 𝑥

+cos 𝑥sin 𝑥

=¿

Case 4: Adding Trig Expressions. Perform the addition and simplify.

Case 5: Rewrite the given expression that is not in fractional form.

11+sin 𝑥

=¿

Case 5: Rewrite the given expression that is not in fractional form.

𝑠𝑖𝑛2𝑥1−𝑐𝑜𝑠𝑥

=¿