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Math 2412 Assignment #2 1. By referring to Unit Circle, what are the x-intercepts for the graph of the function y = cos x over the interval -2π ≤ x < 2π. 2. Describe a shift and/or reflection that will transform the graph of y = sec x into the graph of y = csc x. 3. Try to calculate sec (π/2) on your calculator. Explain the results. 4. State the amplitude and period of y = -2 sin x. Graph the function over the interval -2π ≤ x ≤ 2π. 5. State the amplitude and period of y = 3 – 2 sin (x/2). Graph the function over the interval 0 ≤ x ≤ 4π. 6. Find the equation of the form y = A cos Bx that produces the graph shown below. [-4π, 8π] by [-5, 5] 7. Graph y = -1 – 2 cos (4x + π) over the interval -π ≤ x ≤ π. 8. If the graph below is a graph of an equation of the form y = A cos (Bx + C), -2π ≤ -C/B ≤ 0, find the equation. [-3π, 5π] by [-½, ½] 9. Find the period of y = 2 csc (x/2). Graph the function over the interval 0 < x < 8π. 10. Find the period and phase shift of y = tan (x – π/2). Graph the function over the interval – π < x < 2π. 11. Find the period and phase shift of y = -3 cot (x – π/4). Graph the function over the interval – π < x < 2π. 1 12. Find the exact value of cos −1 without using a calculator. 2 13. Evaluate arcsin 0.5625 to 4 significant digits using a calculator. 14. Find the exact value of tan −1 −1 3 without using a calculator. 15. Find the exact value of tan(cos −1 1 / 2) without using a calculator. 16. Graph y = cos-1x over the interval –1 ≤ x ≤ 1. 17. Write the expression sin (cos-1x) as an algebraic expression in x free of trigonometric or inverse trigonometric functions. 18. Fill in the blanks with appropriate basic identities: STATEMENT REASON 2 sin x tan 2 x + 1 = +1 cos x sin 2 x = +1 cos 2 x sin 2 x + cos 2 x = cos 2 x 1 = cos 2 x 1 = cos x = sec 2 x (A) _____________ Algebra Algebra (B) ______________ 2 Algebra (C) _______________