Trig Final

u=7i+9j and v=-14i7j

-161

Find the unit vector that has the same direction as the vector v. v=-3i+j

-3/sqrt10 i + 1/sqrt10 j

u=-11i-2j,v=4i+7j, find 5u-3v

-67i-31j

Write the vector v in terms of i and j whose magnitude ||v|| and direction angle ø are given. ||v|| = 7, ø=225°

-7sqrt2/2 i - 2sqrt2/2 j

cos(π-x)=-cosx

-cosx=-cosx

Use a calculator to solve the equation on the interval. Round the answer to two decimal places. sinx=0.31 (use sin-1 in calculator)

0.32,2.82

Use a calculator to find the value of the trigonometric function to four decimal places. cos(π/10) (put in radian mode)

0.9511

verify the identy. cotø secø sinø =1

1

Use half-angle formula to find the exact value of the expression. Sin 165°

1/2 sqrt2-sqrt3

Two tracking stations are on the equator 120 miles apart. A weather balloon is location on a bearing of N43°E from the weather station and on a bearing of N19°W from the eastern stations. How far is the balloon from the western station

128.5mi

Two airplanes leave an airport at the same time, one flyinh on a bearing of S45°W at 425mph, and the other flying east at 330mph. How far apart are the planes after 2 hours?

1397 miles

Find the product of the complex numbers. Leave in polar form z1=3(cos40°+isin40°) z1=5(cos55°+isin55°)

15(cos95+isin95)

A water wheel has a radius of 12 feet. The wheel is rotation at 20 revs per minute, find the liner speed, in feet per minute.

1507ft/m

Find the value of each expression in positive degrees. Sin-1(-sqrt2/2)

315degrees

tanø=24/7 in Q3 find sin2ø

336/635

A person is pulling a freight cart with a force of 51 pounds. How much work is done in moving the cart 80 feet if the cart's handle makes an angle of 16° with the ground

3921.9

Find the angle of least positive measure that is co terminal with the following angel. 23π/5

3π/5

Rewrite the expression as an equivalent expression that doesn't contain powers of trig functions greater than 1. 8cos^2x

4+4cos2x

u=-6i-6j,v=10i+9j

4i+3j

Find the quotient z1/z2 of the complex numbers z1=15(cos120°+isin120°) z2=3(cos36°+isin36°)

5(cos84+isin84)

5sin^2xcos^2x

5/8-5/8cos4x

Covert degree measure to radian, and radian to degrees, 58 degrees, and π/9

58 degrees = 29π/90, and 20 degrees

Find the value of each expression in positive degrees. Tan-1(sqrt3)

60 degrees

Use hero's formula to find the area of a triangle. a=14 metres, b=20 metres, c=10metres

65m2

Find the area of the triangle having the given measurements. C=110°, a=9yds, b=9yds

8.46sqyd

Convert the following to a decimal degrees. 83°23'31"

83.392°

sina=8/17 in Q2, and cosB=3/5 in Q1, find sin(a-B)

84/85

Use the properties of even and add functions to answer. sin(π/3)=sqrt3/2 --> sin(-π/3)=?

=-sqrt3/2

Use dot product to determine whether the vectors are parallel, or orthogonal. v=-2i+5j, w=-6i-27j

=0, ORTHOGONAL

Solve the triangles. a=8, b=5, c=4

A=125.1°, B=30.75°, C=24.15°

Solve the triangles. B=13°, b=7.1, a=7.89

A=14.5, C=165.63°, c=7.9

Solve the triangles. A=59°, C=25°, a=28

B=96°, b=32.5°, c=13.8

Find the exast value of the periodic trig function cos(7π/3)

Cos 1/2 (π/3)

1+cos2x/sin2x=?

Cotx

Two forces, F1 and F2, of magnitude 60 and 70 pounds act an on object. The direction of F1 is N40°E and the direction of F2 is N40°W. Find the magnitude and direction angle of the resultant force.

F=99.79cos93.7°i+99.79sin93.7°j

Solve the triangles. A=75°, a=4, b=8

NO TRIANGLE

Find a co function with the same value as the given expression. cos43 degrees

Sin 47 degrees

Let P = (6,-5) be a point on the terminal side of ø .

Sin = -5sqrt61/61 Cos = 6sqrt61/61 Tan=5/6

Write the complex number in polar form. 12+9i

Z=15(cos36.9+isin36.9)

Solve the triangles. b=14, c=9, A=88°

a=16.4, B=58.6°, C=33.4°

cos(a+B)/cosasinB=cotB-tana

cotB-tana

Find the Arc Length r=94in. theta=65 degrees, s=?

s=33.9π inches

Find the area of the sector of a circle. r=3.5mi, ø=5π/6. sA=?

sA=16 mi

sinx/cosx + cosx/sinx=?

secxsecx

cos(π/3+π/4)

sqrt2-sqrt6/4

Sketch the vector as a position. v=-3i+5j

sqrt34

Let cos theta = 4/9 and tan theta<0. Find sin ø

sqrt65/9

Let v be the vector from initial point P1 to point P2. P1=(2,-5), P2=(6,9)

v=4i+14j

The angle from the ground 200 feet away from a building to the top of the building is 32 degrees. How tall is the building?

y~~125ft

Find the angle between the given vectors. v=-2i+5j, w=3i+6j

ø =48.4°

Find reference angle. 320 degrees

ø' = 40 degrees

Find reference angle. 4π/3

ø' = π/3

Find reference angle. 5π/6

ø' = π/6

Use a calculator to find the value of the acute angle theta to the nearest degree. tan ø =4.2856 (use inverse tan, degree mode)

ø= .075

A building that is 450 feet high casts a shadow 140 feet long. Find the angle of elevation to the sun.

ø~~ 72.7 degrees

Solve the following equations on the interval. cos^2x+2cosx+1=0

π

Solve the following equations on the interval. sin(x+7π/6)-sin(x-7π/6)=1

π

Solve the following equations on the interval. sin^2x=4sinx-3

π/2

Find all solutions of the equation. 2cosx-1=0

π/3+2nπ, 5π/3+2nπ

Solve the following equations on the interval. sinx-2sinxcosx=0

π/3,5π/3

8sinx-9sqrt2=6sinx-8sqrt2

π/4+2nπ, 3π/4+2nπ

Solve the following equations on the interval. 2 cos^2x+sinx-2=0

π/6, 5π/6

Solve the following equations on the interval. sin 2x=sqrt3/2

π/6,π/3,7π/6,4π/3