MATH 142 - Review #3 (4986576)
[Pages:10]MATH 142 - Review #3 (4986576)
Question
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Description This is the review for Exam #3. Please work as many problems as possible before we review in-class. As always, if you need anything, please email me Joshua.Patterson@tamuc.edu
1.
Question Details
Write the trigonometric expression in terms of sine and cosine, and then simplify. cos t csc t
2.
Question Details
Write the trigonometric expression in terms of sine and cosine, and then simplify. sin u tan u + cos u
3.
Question Details
Write the trigonometric expression in terms of sine and cosine, and then simplify.
sin2 (1 + cot2 )
4.
Question Details
Write the trigonometric expression in terms of sine and cosine, and then simplify.
csc - sin cos
5.
Question Details
Simplify the trigonometric expression.
cos y + 1 1 + sec y
SPreCalc6 7.1.004. [2703858] SPreCalc6 7.1.009. [2703875] SPreCalc6 7.1.010. [2705111] SPreCalc6 7.1.011. [2703846] SPreCalc6 7.1.015. [2703802] -
6.
Question Details
Simplify the trigonometric expression.
csc2 x - 1 csc2 x
7.
Question Details
Verify the identity.
sin w
= tan w
cos w + sin w tan w + 1
Key: Show your work.
8.
Question Details
Verify the identity. 1 + sec2 x = 1 + cos2 x 1 + tan2 x
Key: Show your work.
9.
Question Details
Verify the identity. sin A + cot A = csc A
1 + cos A
Key: Show your work.
SPreCalc6 7.1.017. [2703798] SPreCalc6 7.1.058. [1719003] SPreCalc6 7.1.062. [1719017] SPreCalc6 7.1.066. [1719027] -
10.
Question Details
Verify the identity. 1 + cot x = tan x + 1 1 - cot x tan x - 1
SPreCalc6 7.1.084. [1719252] -
Key: Show your work.
11.
Question Details
SPreCalc6 7.2.003. [2708358] -
Use an Addition or Subtraction Formula to find the exact value of the expression, as demonstrated in Example 1.
sin 105?
12.
Question Details
SPreCalc6 7.2.006. [2708244] -
Use an Addition or Subtraction Formula to find the exact value of the expression, as demonstrated in Example 1.
cos 165?
13.
Question Details
SPreCalc6 7.2.015. [2708250] -
Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number.
sin 12? cos 48? + cos 12? sin 48?
Find its exact value.
14.
Question Details
SPreCalc6 7.2.017. [2708345] -
Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number.
cos 3 cos 4 + sin 3 sin 4
5
15
5
15
Find its exact value.
15.
Question Details
Prove the identity. cos(x + y) + cos(x - y) = 2 cos x cos y
SPreCalc6 7.2.034.MI. [2678438] -
Key: cos(x + y) + cos(x - y) = cos x cos y - sin x sin y + cos x cos y + sin x sin y = 2 cos x cos y
16.
Question Details
Prove the identity. cot(x + y) = cot y cot x - 1 cot y + cot x
SPreCalc6 7.2.036. [1759351] -
Key: Show your work.
17.
Question Details
Find sin 2x, cos 2x, and tan 2x from the given information. tan x = - 15 , x in Quadrant II 8
sin 2x =
cos 2x =
tan 2x =
18.
Question Details
Find sin 2x, cos 2x, and tan 2x from the given information. csc x = 6, tan x < 0
sin 2x =
cos 2x =
tan 2x =
SPreCalc6 7.3.004. [2708211] SPreCalc6 7.3.006.MI. [2678458] -
19.
Question Details
Find sin 2x, cos 2x, and tan 2x from the given information. tan x = - 1 , cos x > 0 3
sin 2x =
cos 2x =
tan 2x =
20.
Question Details
Use an appropriate Half-Angle Formula to find the exact value of the expression. cos 15?
21.
Question Details
Use an appropriate Half-Angle Formula to find the exact value of the expression.
sin 12
22.
Question Details
Find the rectangular coordinates for the point whose polar coordinates are given.
-1, 5
2
(x, y) =
23.
Question Details
Find the rectangular coordinates for the point whose polar coordinates are given.
(7, 7)
(x, y) =
24.
Question Details
Find the rectangular coordinates for the point whose polar coordinates are given.
8 2, 11
6
(x, y) =
SPreCalc6 7.3.009. [2708228] -
SPreCalc6 7.3.017. [2709806] SPreCalc6 7.3.025. [2709702] SPreCalc6 8.1.030. [2694693] SPreCalc6 8.1.031. [2694689] SPreCalc6 8.1.033. [2694712] -
25.
Question Details
Find the rectangular coordinates for the point whose polar coordinates are given.
3, - 5
3
(x, y) =
SPreCalc6 8.1.034. [2694700] -
26.
Question Details
SPreCalc6 8.1.035-042.501.XP.MI. [1870983] -
A point in rectangular coordinates is given. Convert the point to polar coordinates (r > 0, 0 < 2).
(-7, -7)
(r, ) =
,
27.
Question Details
Convert the rectangular coordinates to polar coordinates with r > 0 and 0 < 2.
(6, -6)
(r, ) =
SPreCalc6 8.1.035. [2694697] -
28.
Question Details
Convert the rectangular coordinates to polar coordinates with r > 0 and 0 < 2.
9 3, -9
(r, ) =
SPreCalc6 8.1.036.MI. [2705979] -
29.
Question Details
Convert the rectangular coordinates to polar coordinates with r > 0 and 0 < 2.
- 6, - 2
(r, ) =
SPreCalc6 8.1.038. [2694694] -
30.
Question Details
Sketch a graph of the polar equation. r = 2
SPreCalc6 8.2.017. [2706031] -
Express the equation in rectangular coordinates. (Use variables x and y.)
31.
Question Details
Sketch a graph of the polar equation.
= 5
6
SPreCalc6 8.2.020. [2708271] -
Express the equation in rectangular coordinates. (Use variables x and y.)
32.
Question Details
Write the complex number in polar form with argument between 0 and 2.
8 + 8i
SPreCalc6 8.3.029. [1785079] -
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