## trig study guide

(7 ∏)/12 radians correspond to degrees.
105

330 degrees correspond to (11∏)/6 radians.
true

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

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

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.
4∏/5

Find the value of cot (120°)
−√(3) / 3

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

The value of sec ∏ is − 1
true

The period for y = − 2 cos ( 3x) is 2/3
false, The period is 2∏/3

The phase shift for y = − 2 cos ( 3x) is

If θ= ∏/4 csc2θ equals
2

Find the exact value of sin (11∏/3)
−√(3) / 2

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

Find the exact value of sin(−5∏/4)
√(2) / 2

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

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

330 degrees correspond to (11∏)/6 radians.
true

Find sin α, given that cos α = − 4/5 and α is in quadrant III
-3/5

The value of sec ∏ is −1
true

The phase shift for y = − 2 cos ( 3x) is

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.
y = − cos ( x + ∏/6) − 2

Find the values of the six trigonometric functions of the angle α in standard position with the terminal side containing the point (7, −24)
tan α = -24/7
sin α = -24/25
cot α = -7/24
sec α = 25/7
csc α = -25/24
cos α = 7/25

The exact value for sec −1(√2) is ∏/3
false, sec −1(√2) is ∏/4

The exact value in degrees for cos−1[√(3)/2] is
30

The exact value for sec −1(√2) is ∏/3
false, sec −1(√2) is ∏/4

The exact value in degrees for cos−1[√(3)/2] is
30

Find the inverse function for f(x) = sin(2x), -∏/4 ≤ x ≤∏/4
f-1(x)= 0.5 sin -1 (x)

cos2 θ tan 2 θ = sin2 θ is an identity.
true

cos(sin−1x) equals √(1 + x2)
false, It equals √(1 − x2)

The exact value for cot −1(√3) is 75 degrees
false, The value is 30

sin θ[csc θ − sin (−θ)] = 1 + sin2 θ is an identity
true

Find the inverse function for f(x) = cos(3x), 0 ≤ x ≤∏/3
f-1(x)= (1/3) cos-1 (x)

Using basic identities the simplified expression for cotx / cscx equals
cosx

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.
188.39

Find sin 2t,if sin t = 4/5 and t is in QUAD I.
24/25

When sin α = −4/5 and cos β = 12/13 with α in quadrant III and β in quadrant IV, then the exact value for sin(α − β) equals
-63/65

Write as the sine or cosine of a single angle cos 3y cos y− sin 3y sin y
cos4y

Write as the sine or cosine of a single angle sin 55° cos 10°− cos 55°sin 10°
sin45

Find all real numbers in the interval [0,2∏) that satisfy the equation
sin2 x − cos2 x = 0
∏/4, 3∏/4, 5∏/4, 7∏/4

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

Find cos 2t if sin t = 4/5 and t is in QUAD I.
-7/25

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

Use a cofunction to fill in the blank for angles in degrees. Enter a number with no spaces: cos(15)=sin()
75

If sin (α/2) = 4/5 and α/2 is in QUADRANT II then sin α=
-24/25

Simplify using sum or difference formulas cos 7x cos x − sin 7x sin x.
cos8x

If sin (α/2) = 4/5 and α/2 is in QUADRANT II then sec α=
-25/7

Write as the sine or cosine of a single angle sin 55° cos 10°− cos 55°sin 10°
sin45

Find all real numbers in the interval [0,2∏) that satisfy the equation
2sin2 x + sin x = 1
∏/6, 3∏/2, 5∏/6

Approximate the area of a triangle with a = 5.4, b = 8.2, c = 12.
18.7

Approximate the area of a triangle with b = 42.7, c = 64.1 and α= 74.2°.
1316.8

If α =30.6°, b = 3.9 and β=94.7 ° use the law of sines to approximate a,c, and γ for the triangle ABC.
γ=54.7, a= 2.0 c=3.2

If β =62°, γ= 77.8°, a = 7.5 use the law of cosines to approximate b and α for the triangle ABC.
b=10.3 and α=40.2

Approximate the area of a triangle with a = 5.4, b = 8.2, c = 12 . Use Heron’s formula.
18.7

Given the complex number z = 5(cos [∏/7] + i sin[∏/7]) the product of z and its complex conjugate is
25

If α =30.6°, b = 3.9 and β=94.7 ° use the law of sines to approximate a,c, and γ for the triangle ABC.
γ=54.7, a= 2.0 c=3.2

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
<2,7> <7,-2> = 90
<-1,5> <2,7> = 27.3
<-2,-5> <1,-9> = 28.1
<2,3> <1,5> = 22.4

There are two triangles with β=28.6, a = 40.7 and b = 52.5.
false, There is only one and α=21.8, γ=129.6 and c = 84.5

Write the complex number −2 − 2i √(3) in trig form
4(cos 240 + i sin 240)

If β =62°, γ= 77.8°, a = 7.5 use the law of cosines to approximate b and α for the triangle ABC.
b=10.3 and α=40.2

The absolute value or lentgh for −2 + 2 i √(3) is
4

Write the vector <2,5> as a linear combination ai+bj of the unit vectors i and j
2i+5j

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
[7√(74)−49]/5

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

Convert the rectangular coordinates ( −2,0) to polar coordinates
(2, 180°)

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

Use De Moivre’s Theorem to simplify 2(cos (45) + i sin (45) ) 5
−16√2 − 16i √2

Write the equivalent rectangular equation for the polar equation r = 2 sin θ
x2 + y2 − 2 y = 0

Eliminate the parameter and write the rectangular system equivalent for
x = t − 5, y = t2 − 10t + 25
y = x2 a parabola

Find the equation of the parabola with vertex (2,3) and directrix y = 5
y = ( − 1/8) ( x − 2 )2 + 3

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

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

The asymptotes for the hyperbola 9×2 − 25 y2 = 225 are
y = ± (3/5) x

The foci of the ellipse 9 x 2 + 25 y2 = 225 are
( ±4 , 0)

(2√3 − 2i)5 = −a√3 − a i with a =
512

Convert the rectangular coordinates ( −2,0) to polar coordinates
(2, 180°)

Eliminate the parameter and write the rectangular system equivalent for
x = t − 5, y = t2 − 10t + 25
y = x2 a parabola

Find the equation of the parabola with vertex (2,3) and directrix y = 5
y = ( − 1/8) ( x − 2 )2 + 3

The asymptotes for the hyperbola 9×2 − 25 y2 = 225 are
y = ± (3/5) x

The foci of the ellipse 9 x 2 + 25 y2 = 225 are
( ±4 , 0)

The fourth roots of 16 are ± p and ±pi with p =
2

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

Use De Moivre’s Theorem to simplify 2(cos (45) + i sin (45) ) 5
−16√2 − 16i √2

Write the equivalent rectangular equation for the polar equation r = 2 sin θ
x2 + y2 − 2 y = 0

330 ° are 11 ∏/6 radians
True

A central angle α 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
7/5

Using basic identities the simplified expression for cotx / cscx equals
cosx

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)
cos4y

Write the complex number −2 − 2i √(3) in trig form
4(cos 240 + i sin 240)

Write the equivalent rectangular equation for the polar equation r = 2 sin θ
x2 + y2 − 2 y = 0

7 ∏/12 radians are equivalent to
105

sin θ[csc θ − sin (−θ)] = 1 + sin2 θ is an identity
True

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

Find cos 2t if sin t = 4/5 and t is in QUAD I.
-7/25

Given the complex number z = 5(cos [∏/7] + i sin[∏/7]) the product of z and its complex conjugate is
25

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

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

The absolute value or lentgh for −2 + 2 i √(3) is
4

The asymptotes for the hyperbola 9×2 − 25 y2 = 225 are
y = ± (3/5) x

The exact value for sec −1(2) is ∏/3
True

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

The fourth roots of 16 are ± p and ±pi with p =
2

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

There are two triangles with β=28.6, a = 40.7 and b = 52.5.
False, There is only one and α=21.8, γ=129.6 and c = 84.5

The phase shift for y = − 2 cos ( 3x) is

Use basic identities to simplify the expression sec θ − cos θ
sin θ tan θ

Use De Moivre’s Theorem to simplify 2(cos (45) + i sin (45) ) 5
−16√2 − 16i √2

Approximate the area of a triangle with a = 12, b = 8, c = 17 . Use Heron’s formula. Select the closest number.
43.5

Calculate without calculators sin (tan -1 (√3/2))
False, The answer is √(21)/7

Convert the rectangular coordinates ( −2,0) to polar coordinates
(2, 180°)

cos(sin−1x) equals √(1 + x2)
False, It equals √(1 − x2)

Eliminate the parameter and write the rectangular system equivalent for x = t − 5, y = t2 − 10t + 25
y = x2 a parabola

Find the component form for the vector with magnitude |v|=12 and direction angle 120°
<−6, 6√(3) >

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)
188.39

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