MATH 142 - Review #3 (4986576) - TAMUC

[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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