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