question

(7 ?)/12 radians correspond to degrees.

answer

105

question

330 degrees correspond to (11?)/6 radians.

answer

true

question

Find the exact length of the arc intercepted by a central angle of 60 degrees in a circle with radius 30 feet.

answer

10 ? feet

question

The terminal side for the angle 7?/6 in the standard position is on the quadrant.

answer

third

question

A one-speed bicycle has two sprockets of radii two and five inches respectively. If somebody is riding the bike and the smaller sprocket rotates a complete turn, find the angle in radians rotated by the larger sprocket.

answer

4?/5

question

Find the value of cot (120°)

answer

??(3) / 3

question

The amplitude for y = ? 2 cos ( 3x) is

answer

2

question

The value of sec ? is ? 1

answer

true

question

The period for y = ? 2 cos ( 3x) is 2/3

answer

false, The period is 2?/3

question

If ?= ?/4 csc2? equals

answer

2

question

Find the exact value of sin (11?/3)

answer

??(3) / 2

question

A central angle ? is subtended in a circle with a radius of 5 inches, by an arc of 7 inches. Calculate the angle in radians.

answer

7/5

question

Find the exact value of sin(?5?/4)

answer

?(2) / 2

question

The period for y = 2 sin (?x/4 + ?) is 8 and the phase—shift is ?4

answer

true

question

The amplitude for y = ? 2 cos ( 3x) is.

answer

2

question

330 degrees correspond to (11?)/6 radians.

answer

true

question

Find sin ?, given that cos ? = ? 4/5 and ? is in quadrant III

answer

-3/5

question

The value of sec ? is ?1

answer

true

question

The graph of y = cos (x) is shifted a distance of ?/6 to the left, reflected in the x-axis, then translated two units downward. Find the equation for the curve in its final position.

answer

y = ? cos ( x + ?/6) ? 2

question

Find the values of the six trigonometric functions of the angle ? in standard position with the terminal side containing the point (7, ?24)

answer

tan ? = -24/7 sin ? = -24/25 cot ? = -7/24 sec ? = 25/7 csc ? = -25/24 cos ? = 7/25

question

The exact value for sec ?1(?2) is ?/3

answer

false, sec ?1(?2) is ?/4

question

The exact value in degrees for cos?1[?(3)/2] is

answer

30

question

The exact value for sec ?1(?2) is ?/3

answer

false, sec ?1(?2) is ?/4

question

The exact value in degrees for cos?1[?(3)/2] is

answer

30

question

Find the inverse function for f(x) = sin(2x), -?/4 ? x ??/4

answer

f-1(x)= 0.5 sin -1 (x)

question

cos2 ? tan 2 ? = sin2 ? is an identity.

answer

true

question

cos(sin?1x) equals ?(1 + x2)

answer

false, It equals ?(1 ? x2)

question

The exact value for cot ?1(?3) is 75 degrees

answer

false, The value is 30

question

sin ?[csc ? ? sin (??)] = 1 + sin2 ? is an identity

answer

true

question

Find the inverse function for f(x) = cos(3x), 0 ? x ??/3

answer

f-1(x)= (1/3) cos-1 (x)

question

Using basic identities the simplified expression for cotx / cscx equals

answer

cosx

question

Two tourists, standing on the same side of and in line with the Washington monument, are looking at its top. The angle of elevation from the first tourist is 33.8 °, and from the second is 59.4 °. If the two tourists stand on level ground and are 170 meters apart, approximate in meters the altitude of the monument.

answer

188.39

question

Find sin 2t,if sin t = 4/5 and t is in QUAD I.

answer

24/25

question

When sin ? = ?4/5 and cos ? = 12/13 with ? in quadrant III and ? in quadrant IV, then the exact value for sin(? ? ?) equals

answer

-63/65

question

Write as the sine or cosine of a single angle cos 3y cos y? sin 3y sin y

answer

cos4y

question

Write as the sine or cosine of a single angle sin 55° cos 10°? cos 55°sin 10°

answer

sin45

question

Find all real numbers in the interval [0,2?) that satisfy the equation sin2 x ? cos2 x = 0

answer

?/4, 3?/4, 5?/4, 7?/4

question

(sin 3 t?sin t)/(cos 3 t+cos t) = tan

answer

t

question

Find cos 2t if sin t = 4/5 and t is in QUAD I.

answer

-7/25

question

Rewrite using sum-to-product formulas sin 3 t + sin 2 t 2 sin (5t/2) cos (t/2)

answer

true

question

Use a cofunction to fill in the blank for angles in degrees. Enter a number with no spaces: cos(15)=sin()

answer

75

question

If sin (?/2) = 4/5 and ?/2 is in QUADRANT II then sin ?=

answer

-24/25

question

Simplify using sum or difference formulas cos 7x cos x ? sin 7x sin x.

answer

cos8x

question

If sin (?/2) = 4/5 and ?/2 is in QUADRANT II then sec ?=

answer

-25/7

question

Write as the sine or cosine of a single angle sin 55° cos 10°? cos 55°sin 10°

answer

sin45

question

Find all real numbers in the interval [0,2?) that satisfy the equation 2sin2 x + sin x = 1

answer

?/6, 3?/2, 5?/6

question

Approximate the area of a triangle with a = 5.4, b = 8.2, c = 12.

answer

18.7

question

Approximate the area of a triangle with b = 42.7, c = 64.1 and ?= 74.2°.

answer

1316.8

question

If ? =30.6°, b = 3.9 and ?=94.7 ° use the law of sines to approximate a,c, and ? for the triangle ABC.

answer

?=54.7, a= 2.0 c=3.2

question

If ? =62°, ?= 77.8°, a = 7.5 use the law of cosines to approximate b and ? for the triangle ABC.

answer

b=10.3 and ?=40.2

question

Approximate the area of a triangle with a = 5.4, b = 8.2, c = 12 . Use Heron's formula.

answer

18.7

question

Given the complex number z = 5(cos [?/7] + i sin[?/7]) the product of z and its complex conjugate is

answer

25

question

If ? =30.6°, b = 3.9 and ?=94.7 ° use the law of sines to approximate a,c, and ? for the triangle ABC.

answer

?=54.7, a= 2.0 c=3.2

question

One column lists pairs of two vectors (a,b) and the other lists the angle between the two vectors to the nearest degree. Correctly match the vector to the angle

answer

= 90 = 27.3 = 28.1 = 22.4

question

There are two triangles with ?=28.6, a = 40.7 and b = 52.5.

answer

false, There is only one and ?=21.8, ?=129.6 and c = 84.5

question

Write the complex number ?2 ? 2i ?(3) in trig form

answer

4(cos 240 + i sin 240)

question

If ? =62°, ?= 77.8°, a = 7.5 use the law of cosines to approximate b and ? for the triangle ABC.

answer

b=10.3 and ?=40.2

question

The absolute value or lentgh for ?2 + 2 i ?(3) is

answer

4

question

Write the vector as a linear combination ai+bj of the unit vectors i and j

answer

2i+5j

question

In the figure Angle A is 90 degrees and the segment BD bisects angle at B. If AC is 5 and AB is 7 calculate AD

answer

[7?(74)?49]/5

question

Convert the polar coordinates (2, ?/4) to rectangular coordinates.

answer

2

question

Convert the rectangular coordinates ( ?2,0) to polar coordinates

answer

(2, 180°)

question

The solutions to x2 + 2i = 0 are ? 1+ i and 1 ? i

answer

true

question

Use De Moivre's Theorem to simplify 2(cos (45) + i sin (45) ) 5

answer

?16?2 ? 16i ?2

question

Write the equivalent rectangular equation for the polar equation r = 2 sin ?

answer

x2 + y2 ? 2 y = 0

question

Eliminate the parameter and write the rectangular system equivalent for x = t ? 5, y = t2 ? 10t + 25

answer

y = x2 a parabola

question

Find the equation of the parabola with vertex (2,3) and directrix y = 5

answer

y = ( ? 1/8) ( x ? 2 )2 + 3

question

The focus for the parabola y = (x ? 1)2 is (1, 1/4)

answer

true

question

The directrix for the parabola y = (x ? 1)2 is y = ?1/4

answer

true

question

The asymptotes for the hyperbola 9x2 ? 25 y2 = 225 are

answer

y = ± (3/5) x

question

The foci of the ellipse 9 x 2 + 25 y2 = 225 are

answer

( ±4 , 0)

question

(2?3 ? 2i)5 = ?a?3 ? a i with a =

answer

512

question

Convert the rectangular coordinates ( ?2,0) to polar coordinates

answer

(2, 180°)

question

Eliminate the parameter and write the rectangular system equivalent for x = t ? 5, y = t2 ? 10t + 25

answer

y = x2 a parabola

question

Find the equation of the parabola with vertex (2,3) and directrix y = 5

answer

y = ( ? 1/8) ( x ? 2 )2 + 3

question

The asymptotes for the hyperbola 9x2 ? 25 y2 = 225 are

answer

y = ± (3/5) x

question

The foci of the ellipse 9 x 2 + 25 y2 = 225 are

answer

( ±4 , 0)

question

The fourth roots of 16 are ± p and ±pi with p =

answer

2

question

The directrix for the parabola y = (x ? 1)2 is y = ?1/4

answer

True

question

Use De Moivre's Theorem to simplify 2(cos (45) + i sin (45) ) 5

answer

?16?2 ? 16i ?2

question

Write the equivalent rectangular equation for the polar equation r = 2 sin ?

answer

x2 + y2 ? 2 y = 0

question

330 ° are 11 ?/6 radians

answer

True

question

A central angle ? is subtended in a circle with a radius of 5 inches, by an arc of 7 inches. Calculate the angle in radians. Enter a fraction as a/b with no spaces or period

answer

7/5

question

Using basic identities the simplified expression for cotx / cscx equals

answer

cosx

question

Write as the sine or cosine of a single angle cos 3y cos y? sin 3y sin y(Enter sin or cos of a single angle in degrees with no space, periods or degree sign as sinz or cos5x)

answer

cos4y

question

Write the complex number ?2 ? 2i ?(3) in trig form

answer

4(cos 240 + i sin 240)

question

Write the equivalent rectangular equation for the polar equation r = 2 sin ?

answer

x2 + y2 ? 2 y = 0

question

7 ?/12 radians are equivalent to

answer

105

question

sin ?[csc ? ? sin (??)] = 1 + sin2 ? is an identity

answer

True

question

The period for y = 2 sin (?x/4 + ?) is 8 and the phase—shift is ?4

answer

True

question

Find cos 2t if sin t = 4/5 and t is in QUAD I.

answer

-7/25

question

Given the complex number z = 5(cos [?/7] + i sin[?/7]) the product of z and its complex conjugate is

answer

25

question

If sin (?/2) = 4/5 and ?/2 is in QUADRANT II then tan ?=

answer

24/7

question

Rewrite using sum-to-product formulas sin 3 t + sin 2 t Answer: 2 sin (5t/2) cos (t/2)

answer

True

question

The absolute value or lentgh for ?2 + 2 i ?(3) is

answer

4

question

The asymptotes for the hyperbola 9x2 ? 25 y2 = 225 are

answer

y = ± (3/5) x

question

The exact value for sec ?1(2) is ?/3

answer

True

question

The focus for the parabola y = (x ? 1)2 is (1, 1/4)

answer

True

question

The fourth roots of 16 are ± p and ±pi with p =

answer

2

question

The terminal side for the angle 7?/6 in the standard position is on the

answer

third

question

There are two triangles with ?=28.6, a = 40.7 and b = 52.5.

answer

False, There is only one and ?=21.8, ?=129.6 and c = 84.5

question

Use basic identities to simplify the expression sec ? ? cos ?

answer

sin ? tan ?

question

Use De Moivre's Theorem to simplify 2(cos (45) + i sin (45) ) 5

answer

?16?2 ? 16i ?2

question

Approximate the area of a triangle with a = 12, b = 8, c = 17 . Use Heron's formula. Select the closest number.

answer

43.5

question

Calculate without calculators sin (tan -1 (?3/2)) Answer: 5/7

answer

False, The answer is ?(21)/7

question

Convert the rectangular coordinates ( ?2,0) to polar coordinates

answer

(2, 180°)

question

cos(sin?1x) equals ?(1 + x2)

answer

False, It equals ?(1 ? x2)

question

Eliminate the parameter and write the rectangular system equivalent for x = t ? 5, y = t2 ? 10t + 25

answer

y = x2 a parabola

question

Two tourists, standing on the same side of and in line with the Washington monument, are looking at its top. The angle of elevation from the first tourist is 33.8 °, and from the second is 59.4 °. If the two tourists stand on level ground and are 170 meters apart, approximate in meters the altitude of the monument. (Neglect the tourist's heights. Round up to two decimals)

answer

188.39

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