Trig final

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Given the graph of y=asinb(x+c)+d, determine the vertical displacement

-1

Find the exact value of the given expression cos(60+135)

-1-sqrt3/2 sqrt2

use a calculator to evaluate tan39 22' round your answer to four decimal places

0.8204

what is the phase shift of the function y=sin(3x+3)

1 unit left

if B=29degrees and a=9, determine the value of c. Round to two decimal places

10.29

The line of sight from a small boat to the light at the top of a 35-foot lighthouse built on a cliff 25 feet above the water makes a 25 degree angle with the water to the nearest foot, how far is the boat from the cliff?

128 feet

Given the graph of y=asinb(x-c)+d on the right, determine the value of b

2

use a calculator to evaluate tan 245 Round your answer to four decimal places

2.1445

Find the exact value of csc0 using the triangle shown in the figure below if a=24 b=7

25/7

Convert 260 59' 51" to degree decimal form. Round answer to three decimal places

260.998

Determine the quadrant in which a 130 angle lies

2nd quadrant

find the period of the function y=-2cos(3x)+1

2pi/3

Use trig Identities to identify which expression is equivalent to 2/cotx-cscx

2sinx/coxx-1

find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 1- yards tall casts a shadow 14 yards long. Round to the nearest degree

36

Determine the quadrant in which a -150 38' angle lies

3rd quadrant

Find the length of the arc, S, on a circle of radius 7 feet intercepted by a central angle of 330. Round to two decimal places

40.32

Determine the quadrant in which an angle, 0, lies if 0=5.40 radains

4th quadrant

find the length of the hypotenuse

6

Given A=53, B=73, and c=8. fidn the value of a

7.90

rewrite 315 in radian measure as a multiple of pi

7pi/4

using the figure below if 0=26degrees and y=8, etermine the exact value of x

8/tan26

Given a=12, b=11, and c=8. use the Law of Cosines to find the value of C

C=40.42

Find the magnitude of vector v with initial point (3, -6) and terminal point (0,6)

IIvII=3 sqrt17

Find the magnitude of vector v with initial point (7, -7) and terminal point (-1,5)

IIvII=4 sqrt13

Find the magnitude of vector v (4,-3)

IIvII=5

Find the magnitude of vector v with initial point (3,6) and terminal point (-4.-1)

IIvII=7 sqrt2

Given C=130, B=29, and c=15. find the value of a

a=7.02

Given C=123 degrees, B=32 degrees, and c=15. use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places

a=7.56

evaluate arctanspart3/3 without using a calculator

pi/6

Let w be a vector with initial point (-1,7) and terminal point (-4,1) Write w as a linear combination of the standard unit vectors i and j

w=-3i-6j

Given u=(-4,4) and v=(-5,0) determine -6u-2v

-6u-2v=(34,-24)

Find the exact value of the given expression cos(60+135)

-sqrt6-sqrt2/4

Given sin30=1/2 and cos30=pi3/2, determine the following csc30

csc30=2

Given C=100degrees, a=8, and b=7, use the Law of Cosines to solve the triangle for the valuce of c. Round answer to two decimal places.

11.51

Given a=7, b=13, and c=8, use the Law of Cosines to solve the triangle for value of B. Round answer to two decimal places.

120.00

If a=5 and c=20, determine the value of A. Round to two decimal places

14.48

viola drives 170 meters up a hill that makes an angle of 6 with the horizontal, what horizontal has she covered

169.1

Given C=108, a=9, b=15 find the value of c

19.73

determine two coterminal angles for 0=-503

217, -143

fidn the value of x in the triangle below

23

Evaluate cos^-1 (sqrt3/-2) without using a calculator

5pi/6

Find the value of x in the triangle below

6.2

find the measure of x in the right triangle

69.1

A vertical pole 32 feet tall stands on a hillside that makes an angle of 17degrees with the horizontal. Determine the approximate length of cable that would be needed to reach from the top of the pole to a point 56 feet downhill from the base of the pole. Round answer to two decimal places

72.17

Given A=72degrees, b=6, and c=8. Use the Law of Cosines to solve the triangle for the value of a. Round answer to two decimal places.

8.39

rewrite 4pi/9 in degree measure

80

Given u=(1,-5) and v=(-4,-2) determine 9u-v

9u-v=(13,-43)

simplify the expression cosx/1+sinx+tanx using trig identities

secx

Using trig identities to simply the expression sinx/cosx+cosx/sinx Identify an equivalent

secxcscx

write the given expression as the sine of an angle (sin100 cos 35+sin35 cos 100

sin 135

Find the exact value of the given expression using a sum or difference formula cos 19pi/12

sqrt3-1/2 sqrt2

Givne u=(3,4) and v=(-2,5) determine u-6v

u-6v=(15,-26)

Find the vector v that has a magnitude of 4 and is in the same direction as u, where u=(-3,-6)

v(-4/sqrt5, -8/sqrt5)

find the component form of vector v with initial point (3,2) and terminal point (2,6).

v=(-1,4)

Find the component form of vector v with initial point (5,0) and terminal point (-5,-3)

v=(-10,-3)

Fidn the component form of vector v with initial point (2,-7) and terminal point (-6,4)

v=(-8,11)

Find the component form of vector v

v=(4,5)

Let w be a vector with initial point (9,1) and terminal point (5,4). Write w as a linear combination of the standard unit vectors i and j

w=-4i+3j

solve the equation of 2sin^2x=sinx

x=0, pi, pi/6, 5pi/6

fidn the exact solutions of the given equation in the interval [0, 2pi] sin2x=sinx

x=0, pi/3, pi, 5pi/3

Find the value of x and y without using a calculator

x=17 sqrt3. y=34

Solve the multiple-angle equation cosx/2=-sqrt3/2

x=5pi/3+4npi and 7pi/3+4npi, where n is an integer

which of the folowing is a solution to the given equation sqrt2 sinx+1=0

x=7pi/4

which of the following is a solution to the equation 2cosx+sqrt3=0

x=7pi/6

Solve the following equation 2cosx-1=0

x=pi/3+2nPi and x=5pi/3+2npi, where n is an integer

Which one of the equations matches the graph

y=-2sin(3x)

Which one of the equations below matches the graph

y=2sin(1/3x)

The point (-5, -12) is on the terminal side of an angle in standard position. Determine the exact value of tan0

tan0=12/5

write the given expression tan7x-tanx/1+tan7xtanx as a single trig expression

tan6x

If the graph of the function f(x)=5sinx+p just touches the x-axis what is the value of p

-5 or 5

Find the exact value of the given expression using a sum or difference formula sin345

-sqrt3+1/2 sqrt2

Find the exact value of the given expression sin(5pi/3-pi/4)

-sqrt3-1/2 sqrt2

Which of the following is equivalent to the given expression sin^2x/1-cosx

1+cosx

Given a=3 b=11, and c=10, use the Law of Cosines to solve the triangle for the value of A. Round answer to two decimal places

15.50

A radio transmission tower is 100 feet tall. How long should a guy wire be if it is to be attached 7 feet from the top and is to amke and angle of 23 degrees with the ground? Give your answer to the nearest tenth of a foot.

238.0 ft

A granular subastance as sand naturally settles into a cone-shaped pile when poured from a small aperture. Its height depends on the humidity and adhesion between granules. The angle of elevation of a pile, theta, is called the angle of repose. If the height of a pile of sand is 15 feet and its diameter is approximately 52, determine the angle repose. Round answer to nearest degree.

30

Determine the quadrant in which an angle, 0, lies if 0=8pi/7

3rd quadrant

Given u=4i+2j and v=-3i-2j determine 3u-9v

3u-9v=39i+24j

if sin0=sqrt3/2, find the value of 0 in degrees (0<theta<90) without the aid of a calculator

60 degrees

Determine two coterminal angles (one positive and one negative) for 0=2pi/3

8pi/3 -4pi/3

State the quadrant in which 0 lies if sectheta>0 and csctheta<0

Quadrant IV

Find the amplitude and period of y=-4sin(0-6)+7

amplitude: 4, period 2pi

Write the given expression as a single trig expressions (sin95 cos40-sin40 cos 95)

sin55

after a severe storm, three sisters, April, May and June, stood on their porch and noticed that the tree in their front yard was leaning 6 from vertical toward the house. From the porch which is 98 feet away from the base of the three, they noticed that the angle of elevation to the top of the tree was 24. Approximate the height of the tree. Round to two decimal places

41.91

write the given expression as the cosine of an angle (cos60 cos65-sin60 sin 65

cos125

write the expression cos55cos40+sin55sin40 as a single trig expression

cos15

find the exact value of cos 19pi/12 using a sum or difference formula

sqrt6-sqrt2/4

find the exact value of cos(285) using an anglue sum or difference

sqrt6-sqrt2/4

find the exact value of sin11pi/12 using an angle sum or difference

sqrt6-sqrt2/4

write the given expression as the tangent of an angle (tan5x+tan3x/1-tan5x tan3x

tan(8x)

Let w be a vector with initial point (9, -1) and terminal point (-3, 7). Write w as a linear combination of the standard unit vector i and j

w=-12i+8j


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