SparkNotes: Review of Trigonometry: Review Test

Which of the following values has a different sign from the others?

(A) Sine in Quadrant III

(B) Cosine in Quadrant II

(C) Cotangent in Quadrant IV

(D) Secant in Quadrant IV

Which of the following values is unequal to the others?

(A) sin(60^o)

(B) cos(150^o)

(C) cos(330^o)

(D) sin(120^o)

Which of the following angles has a reference angle of 60^o ?

(A) 150^o

(B) -120^o

(C) -210^o

(D) -30^o

An arc along the unit circle begins at (1,0) and is units long. What are the coordinates of its endpoint?

(A) (

,

)

(B) (-

,

)

(C) (-

, -

)

(D) (

,

)

Which of the following graphs is not the same as the others?

(A) y = sin(x - Π)

(B) y = sin(x)

(C) y = cos(x -

)

(D) y = cos(x +

)

Which of the following graphs has a different period from the others?

(A) y = cos(2x)

(B) y = tan(x)

(C) y = sin(2x)

(D) y = csc(x)

Which of the following graphs has a different amplitude from the others?

(A) y = sin(2x)

(B) y = 2 cos(x - Π)

(C) y = cos(x +

)

(D) y = sin(3x) + 2

What fraction of angles has a tangent less than 1?

(A)

(B)

(C)

(D) Impossible to tell--there are an infinite number of angles in existence.

Which of the following is unequal to the others?

(A) sin(x)csc(x)

(B) sec²(x) - tan²(x)

(C) csc²(x) - cot²(x)

(D) sin²(x) - cos²(x)

Which of the following is unequal to the others?

(A) cos(x)tan(x)

(B)

(C)

(D)

Which of the following functions is even?

(A) sine

(B) tangent

(C) cosecant

(D) secant

Which of the following is unequal to the others?

(A)

(B)

(C) sin(x)cos(x)csc(- x)

(D) sin(x)cot(x)

If sin(x) = , what is sin(x) ?

(A)

(B) -

(C)

(D) Impossible to tell

Solve for x . 2 sin(x)cos(x) = 1 .

(A) x =

,

(B) x =

,

(C) x =

(D) Impossible to calculate

Solve for x . sin(x) - = cos(x) .

(A) x =

,

(B) x =

,

(C) x =

,

(D) x =

,

Solve for x . cos(x)tan(x) + 1 = sec²(x) - tan²(x) - 1 .

(A) x =

(B) x =

,

(C) No solution

(D) x =

Solve for x . 2 cos(x) = sin(x)csc(x) .

(A) x = 30^o, 150^o

(B) x = 60^o, 300^o

(C) x = 90^o

(D) x = 45^o, 225^o

Solve for x . sin(x)tan(x)sec(x) = .

(A) x =

(B) x =

,

(C) x =

,

(D) x =

,

Solve for x . = sin²(x) + cos²(x) - sin(x)csc(x) .

(A) x = 0, Π

(B) x =

(C) x =

,

(D) No solution

Solve for x . tan(x)sin(x)cos(x) = sin(x)sec(x) .

(A) x =

,

(B) x = 0,

(C) x =

,

(D) x = 0,

, Π,

Solve for x . 2 cos(x) = - (csc²(x) - )

(A) x =

,

(B) x =

,

(C) x =

,

(D) x =

,

Which of the following numbers is part of the domain of Arcsecant?

(A)

(B)

(C)

(D)

Which of the following is uneequal to the others?

(A) arcsin

(B) arccos

(C) arctan(1)

(D) They're all equal to each other

Which of the following is undefined?

(A) arcsin(

)

(B) arccos(1)

(C) arcsec(

)

(D) arccsc(1)

Solve the right triangle ABC with right angle C given c = 5 , b = 3 .

(A) a = 4 , A

36.9^o , B

53.1^o .

(B) a = 4 , A

53.1^o , B

36.9^o .

(C) a = 4 , A = B = 45^o .

(D) a =

, A

53.1^o , B

36.9^o .

Right triangle ABC has right angle C , A = 30^o , and b = . Find a .

(A) a = 2 .

(B) a = c cos(30)

(C) a = 1

(D) The previous two answers are both right

A boat sails 40^o south of east for 30 miles. How far south and east does it travel?

(A)

23.0 miles south and 19.3 miles east

(B)

19.3 miles east and south

(C)

19.3 miles south and 23.0 miles east

(D)

25.2 miles south and east

An airplane flies 5^o west of north for 240 miles. How far west and north does it travel?

(A)

20 miles west and 220 miles north

(B)

200 miles west and 40 miles north

(C)

20.9 miles west and 239.1 miles north

(D)

239.1 miles west and 20.9 miles north

A 20 foot ladder leans against a wall and forms a 45^o angles with the ground. How high up on the wall does the ladder reach?

(A) 20 feet

(B) 10 feet

(C) 20

feet

(D)

feet

Which of the following right triangles ABC with C = 90^o is not congruent to the others?

(A) a = 6 , B

36.9^o

(B) b = 6 , c = 10

(C) A

53.1^o , B

36.9^o

(D) c = 10 , A

53.1^o

Which of the following right triangles ABC with C = 90^o is not congruent to the others?

(A) c = 2 , B = 30^o

(B) a =

, B = 30^o

(C) b = 1 , A = 60^o

(D) A = 60^o , c =

One boat sails 30 miles west and 22 miles north. Another boat sails 55 miles west and 42 miles north. Which boat traveled in the direction closest to due north?

(A) They both traveled in the same direction

(B) The first boat

(C) The second boat

(D) Impossible to calculate

The sun's rays hit the earth's surface at a 45 degree angle. How long a shadow does a 50 foot tree cast?

(A) 25 feet

(B) 50 feet

(C) 100 feet

(D) 50

feet

A ship's final destination is 310 miles east and 48 miles north. It sails for 260 miles in a direction 22^o south of east to an intermediate destination. What is the required distance and direction for the ship to reach its final destination?

(A)

69.3 miles, 64.6^o north of east

(B)

98 miles, 44^o north of east

(C)

160.9 miles, 44^o north of east

(D)

160.9 miles, 64.6^o north of east

Which of the following triangles ABC is not congruent to the others?

(A) A

23.5^o , B = 130^o , c = 7

(B) B = 130^o , b = 12 , a

6.25

(C) A

23.5^o , c

6.25 , C

26.5^o

(D) b = 12 , A

23.5^o , C

26.5^o

Calculate A given the following information about triangle ABC: a = 12 , b = 14 , B = 40^o .

(A) A

56.6^o

(B) A

.551^o

(C) A

33.4^o

(D) Impossible to calculate

Given b , c , and C of an oblique trianlge, in which C is acute and c < b , how many triangles are determined?

(A) 0

(B) 1 OR 2

(C) 0 OR 2

(D) 0, 1, OR 2

Solve for C , in the following triangle ABC, given that a = 5 , b = 5 , and B = 110^o .

(A) C = 40^o

(B) C

32.3^o

(C) The triangle does not exist

(D) Impossible to calculate

Find angle B of triangle ABC given a = 5 , b = 6 , and c = 7

(A) A

57.1^o

(B) A

32.9^o

(C) A

47.1^o

(D) Impossible to calculate

Find angle B of triangle ABC given that c = 17 and A = 55^o

(A) B = 45^o

(B) B

24.7^o

(C) The triangle does not exist

(D) Impossible to calculate

Find side b in triangle ABC given that a = 18 , c = 21 , and C = 43^o .

(A) b = 20

(B) b

20.6

(C) b

30.2

(D) Impossible to calculate

Find the area of triangle ABC given a = 5 , b = 17 , and c = 19

(A) Area = 20.5

(B) Area

40.8

(C) Area

13.8

(D) Impossible to calculate

Find the area of triangle ABC given a = 5.6 , b = 4.2 , and C = 110^o

(A) Area = 9.8

(B) Area

11.0

(C) Area = 11.76

(D) Area = 23.52

Find the area of triangle ABC given that A = 25^o , B = 135^o , and c = 14 .

(A) Area

42.8

(B) Area = 14

(C) Area

85.6

(D) Area

112.4

Find the area of triangle ABC given that a = 3 , c = 5 , and C = 90^o .

(A) Area = 12

(B) Area = 3

(C) Area = 7.5

(D) Area = 6

Which of the following expressions is unequal to the others?

(A) cos(2x)

(B) 2 sin(x)cos(x)

(C) 2 cos²(x) - 1

(D) 1 - 2 sin²(x)

Which of the following expressions is unequal to the others?

(A) sin(60^o)cos(20^o) + cos(60^o)sin(20^o)

(B) cos(40^o)

(C) cos(60^o)cos(20^o) + sin(60^o)sin(20^o)

(D) cos(60^o)cos(- 20^o) - sin(60^o)sin(- 20^o)

Which of the following expressions is unequal to the others?

(A) cos(β)sin(α)

(B)

(sin(α + β) + sin(α - β))

(C) sin(α)cos(β)

(D)

(sin(α + β) - sin(α - β))

Which of the following expressions is unequal to the others?

(A) sin(x)cos(x)

(B)

sin(2x)

(C) sin²(x)cot²(x)

(D) tan(x)cos²(x)

Which of the following expressions is unequal to the others?

(A)

(B) sin²(x)(1 + cot²(x)

(C)

(D)

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