This Journal entry has two parts:

Part A:SelectTWO examplesof solutions to trig identities from theContentsection (ExamplesorCheck your Understanding) or fromAssignment 1Solutions.

• Annotatethe solution for the example explaining the steps.
• Refer to theTips for Solving Trigonometric Identitiesfrom theContentsection.

Example of Annotated Solution (Number 3 from Assignment 1)

Part B:Make up your OWN identity. Start with a trigonometric expression, and apply substitutions and algebraic processes to create equivalent expressions. Note that this is NOT the same as proving an existing trig identity.

Justify each step. Verify your identity graphically and algebraically.

This checklistwill be used to evaluate your assignment.

Submit your journal to thedropbox.

1. Question Let R be a relation on the set N given by R = {a, b) : a = b - 2, b > 6}. Then A. (2, 4) an B. (3. 8) ER C. {6, 8} ER D. {8. ?} ER 23. Question Mark the correct alternative in each of the following: Consider the binary operation * dened on Q -{1}by the rule a * b - a + b ab for all a. b E Q {1}. The identity element in Q {1} is All 3.1 cl 3 .-1 D i". QuestionLetA = {2, 3, 4, 5. 1?, 18}. Let '2' be the equivalence relation on A x A, cartesian product ofA with itself, dened by (a, b) 2 (c, d) iff ad = be. Then, the number of ordered pairs of the equivalence class of (3, 2) is A. 4 B. 5 C. 6 D. FAnswer 06: The radius of a circle is increasing at the rate of 0.7 cmfs. What is the rate of increase of its circumference? Q1 : Find the rate of change of the area of a circle with respect to its radius rwhen talr=3cmtblr=4cm \f5. Question Mark the correct alternative in each of the following: For the binary operation * on Z dened by a * b = a + b + 1 the identityr element is A. 0 B. -1 C. 1 D. 2 12. Question Mark the correct alternative in each of the following: Which of the following is true? q. A. * defined by a '7' b = a is a binary operation on Z .1 B. * defined by a * b = a is a binary operation on 0 .5 ' C. all binary commutative operations are associative D. subtraction is a binary.r operation on N 19. Question Mari: the correct alternative in each of the following: 0n 2 an operation * is dened by a * b = a2 + t:-2 for all a, b E 2+ The operation * on 2 is A. commutative and associative B. assoclative but not commutative C. not associative [Jr not a binary operation 9. Question The relation 'R' in N x N such that (a, b) R (C. d) a + cl = b + c is A. reflexive but of symmetric B. reflexive and transitive but not symmetric: C. an equivalence relation D. none of these 2. Question Mark the correct alternative in each of the following: Ifa * b denote the bigger among a and b and if a- b = [a t b} + 3. then 4.? = 16. Question Let A = {1, 2, 3} and R = {(1, 2], (2, 3), (1, 3)} be a relation on A. Then, R is A. neither reexive nor transitive B. neither symmetric nor transitive C. transitive D. none ofthese B. Guestion Mark the correct altematiue in each of the following: _>. x _ If G is the set of all matrices of the form '. where x E R {0}. then the identity element with respect ' x s to the multiplicatlon of matrices as oinan} operation. is 1 1 '_1 1.' 1:: .-'2' a. 1 1 '_1.r: 1.-':_ '1 2 1-':" c. | '1': 1*: '1 _1_ D. '1 1' 14. Question Mark the correct alternative in each of the following: If a binary operation * is defined by a * b = a2 + b2 + ab + 1. then (2 * 3} * 2 is equal to A. 20 B. 40 C. 400 D. 445 1'. Question Mark the correct alternative in each of the following: 0+ denote the set of all positive rational numbers. If the binary operation {3 on 0* is dened as a ab , then the inverse of 3 is not): ., Ali 3 5.2 11. Question A relation R is defined form {2, 3, 4, 5} to {3, 6, 7', 10} by va x is relatively prime to v. Then, domain of R is A. {2, 3 5} B. {3, 5} C. {2, 3, 4} D. {2, 3, 4, 5} 17. Question Mark the correct alternative in each of the following: The lawa + b = b + a is called A. closure law B. associative law C. commutative law D. distributive law 26. Question Mark the correct alternative in each of the following: On the set 0+ of all positive rational numbers a binary operation * is dened by a * b = for all a. b E C\". 'I The inverse of 8 is A l 8 3.1 3 (2.2 16. Question Let A = {1, 2, 3} and R = {(1, 2), (2, 3), (1, 3)} be a relation on A. Then, R is A. neither reexive nor transitive B. neither symmetric nor transitive C. transitive D. none ofthese 6. Questlon Mark the correct alternative in each of the following: If a binary operation * is defined on the set 2 of integers as a * b = Ba - b. then the value of (2 1' 3} *4 is A2 5.3 C4 D.5 \f