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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.
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12. Find the exact value of cos −1 without using a calculator.
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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) _______________