Lesson D - Assignment Booklet Mathematics 30-1: Unit 2 Back to Baker Street... Complete the Back to Baker Street assignment. Refer to the Tips From Scotland Yard located at the back of this lesson booklet to assist you in completing the assignment. Please show pertinent work and explanation. Call or e-mail your teacher if you would like additional help. Multiple-Choice Items 1 2 1. The statement about identities that is false is A. the permissible values will always produce identical values on both sides of the equation B. the non-permissible values will always produce identical values on both sides of the equation C. when graphing each side of an identity, the graphs will be identical D. substituting in any value for the angle, other than a non-permissible value, will result in both sides of the equation being equal 2. The expression cos x is equivalent to 1 - sin x A. 1 + sin x cos x B. 1 - sin x cos x C. cos(x)(1 + sin(x)) D. cos(x)(1 - sin(x)) Numeric Response 1 1 76 Given the domain 0c # i # 360c , the smallest non-permissionable value of the identity cos(cos - sec) = cos2 - 1 is Alberta Distance Learning Centre Mathematics 30-1: Unit 2 4 Lesson D - Assignment Booklet 3. The exact value of sin 255 is A. ^- 3 - 1h 2 2 B. ^ h C. - 3 + 1 2 2 D. ^ 3 + 1h 2 2 ^ 3 - 1h 2 2 Numeric Response 2 1 To verify the identity 1 - sincostan = cos2, a student substituted in = 324. To the nearest hundredth, the value of each side of the identity is 1 4. The expression cos(A + ) - sin(A + ) can be simplified to A. sin(A) - cos(A) B. sin(A) + cos(A) C. cos(A) - sin(A) D. -sin(A) - cos(A) Numeric Response 3 2 r Given sin A = 5 and cos B = 4 , where A and B are both between 0 and 2 then to the 13 5 nearest hundredth, sin(B - A) = Alberta Distance Learning Centre 77 Lesson D - Assignment Booklet Mathematics 30-1: Unit 2 Written Response 1. Given the identity csc i sec i = csc2 i , tan i 1 State all restrictions on 2 Verify that the identity is true for i = 1 Graph the two sides of the equation on the grid below in the domain 0 < < 2. 78 Alberta Distance Learning Centre r , using EXACT values. 4 Mathematics 30-1: Unit 2 Lesson D - Assignment Booklet 2. Given the equation: (sin(x) + cos(x))2 = sin2(x) + cos2(x), 1 State all restrictions on x 2 Verify that the equation is identical on each side using x = r . 2 2 Determine, giving a reason, whether this is an identity. Total: 22 Alberta Distance Learning Centre 79 Mathematics 30-1: Unit 2 Lesson D: Trigonometric Identities S Standard of Excellence Students need to make connections to other courses to complete. Successful completion shows an ability to think beyond given examples. O Over the acceptable level of understanding Students need to make connections from within the course notes and example to complete. Successful completion shows an ability to draw from given instruction and apply skills to new problems. L Level of acceptable standards Students need to show acceptable levels of understanding to complete. Successful completion shows ability to follow given examples. V Below level of acceptable standards Student's response to question is below acceptable standard. E Inadequate level of acceptable understanding Student's response to question indicates student needs assistance in understanding basic concepts. Thinkstock 80 Alberta Distance Learning Centre