trig study guide

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

third

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

true

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

true

The value of sec ∏ is −1

true

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

true

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

y = x2 a parabola

Find the exact value of sin (11∏/3)

−√(3) / 2

7 ∏/12 radians are equivalent to

105

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

1316.8

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

18.7

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

18.7

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

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

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

24/25

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

24/7

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

25

Find the component form for the vector with magnitude |v|=12 and direction angle 120°

<−6, 6√(3) >

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

False, The answer is √(21)/7

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

330 ° are 11 ∏/6 radians

True

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

True

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

True

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

True

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

True

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

The exact value for sec −1(√2) is ∏/3

false, sec −1(√2) is ∏/4

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

sin θ tan θ

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

sin45

(sin 3 t−sin t)/(cos 3 t+cos t) = tan

t

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

third

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

true

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

true

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

true

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

true

The value of sec ∏ is − 1

true

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

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

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

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

∏/6, 3∏/2, 5∏/6

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

−16√2 − 16i √2

Find the value of cot (120°)

−√(3) / 3

Find the exact value of sin(−5∏/4)

√(2) / 2

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

2

If θ= ∏/4 csc2θ equals

2

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

2

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

2

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

2

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

( ±4 , 0)

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

(2, 180°)

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

-24/25

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

-25/7

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

-3/5

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

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

-7/25

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

0

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

10 ∏ feet

(7 ∏)/12 radians correspond to degrees.

105

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

2i+5j

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

30

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

4

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

4(cos 240 + i sin 240)

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

43.5

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

(2√3 − 2i)5 = −a√3 − a i with a =

512

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

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

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

cos(sin−1x) equals √(1 + x2)

False, It equals √(1 − x2)

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

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 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

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

cos8x

Using basic identities the simplified expression for cotx / cscx equals

cosx

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

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

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

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

cos(sin−1x) equals √(1 + x2)

false, It equals √(1 − x2)

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

false, The period is 2∏/3

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

false, The value is 30

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

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

75

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

true

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

x2 + y2 − 2 y = 0

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

y = ( − 1/8) ( x − 2 )2 + 3

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

y = x2 a parabola

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

y = ± (3/5) x