1. 5.1(a) Notes: Using Fundamental Identities
Date:
5.1(a) Notes: Using Fundamental Identities
Lesson Objective: Recognize and write the
fundamental trig identities. Use the trig iden-tities to simplify trig expressions.
CCSS: F-TF Extend the domain of tri­go­no­me­tric functions using the unit circle.
You will need: a separate sheet of paper, graphing calculator

2. Lesson 1: Fundamental Trig Identities
On a separate page, write the following iden-tities.

3. Lesson 1: Fundamental Trig Identities
Reciprocal Identities:
sin x = ____ cos x = ____ tan x = ____
csc x = ____ sec x = ____ cot x = ____

4. Lesson 1: Fundamental Trig Identities
Reciprocal Identities:
sin x = ____ cos x = ____ tan x = ____
csc x = ____ sec x = ____ cot x = ____
Quotient Identities:
tan x = ____ cot x = ____

5. Lesson 1: Fundamental Trig Identities
Pythagorean Identities:

6. Lesson 1: Fundamental Trig Identities
Pythagorean Identities:
= 1 

7. Lesson 1: Fundamental Trig Identities
Pythagorean Identities:
= 1
sin x = +
cos x = +
tan x = +
cot x = +

8. Lesson 1: Fundamental Trig Identities
Use a graphing utility to graph the following:
sin x
cos x
sin π 2 −𝑥 = ?

9. Lesson 1: Fundamental Trig Identities
Cofunction Identities:
sin π 2 −𝑥 = cos x cos π 2 −𝑥 =
tan π 2 −𝑥 = cot π 2 −𝑥 =
csc π 2 −𝑥 = sec π 2 −𝑥 =

10. Lesson 1: Fundamental Trig Identities
Even Identities:
cos(-x) =
sec(-x) =
Odd Identities:
sin(-x) =
csc(-x) =
tan(-x) =
cot(-x) =

11. Lesson 2: Using Identities to Evaluate a Function
Use the values sin x = ½ and cos x > 0 to find the values of all six trigonometric functions.

12. Lesson 3: Simplifying a Trig Expression
cos²x csc x – csc x

13. Lesson 3: Simplifying a Trig Expression
csc t – cos t cot t

14. Lesson 4: Factoring Trigonometric Expressions
Factor each expression.
1 – cos²x

15. Lesson 4: Factoring Trigonometric Expressions
Factor each expression.
2 csc²x – 7csc x + 6

16. Lesson 4: Factoring Trigonometric Expressions
Factor each expression.
sec²x + 3 tan x + 1

17. 5.1(a): Do I Get It? Yes or No
Use the values sec u = and tan u > 0 to find the values of all six trig functions.
Simplify sin x cos2x – sin x.
Simplify sin t + cot t cos t.
Factor sec2 θ – 1.
Factor 4 tan2 θ + tan θ – 3.
Factor csc2 x – cot x – 3.