Sine
Cosine
Vectors
Triangles
Polar Graphs/Equations
100
Use the sum and difference formulas to determine exact values of trigonometric expressions and verify identities.
sin(pi/12)
.2588
100
Rewrite the sum as the product of two functions. Give your answer in terms of cosine.
cos(58)+cos(12)
2cos(35)cos(23)
100
Express a vector in component form with P1:(1,5) and P2:(3,9)
(2,4)
100
From the given information, determine if this one, two, or zero triangles can be formed
a=6, b=3, AngleB=24 degrees
Two triangles can be formed
100
Convert the given coordinates from polar coordinates to cartesian coordinates...
(4, pi/3)
(2,2 roots of 3)
200
Evaluate the product using a sum or difference of two functions. Leave in terms of sine
2sin(-100)sin(-20)
cos(80)-cos(120)
200
Find all exact solutions on the interval 0 ≤ 𝜃 < 2𝜋
2cos(theta)=-1
2pi/3, 4pi/3
200
Determine the direction and magnitude of the following vector...< 3,4 >
Magnitude=5
Direction=53.1 degrees
200
Use heron's formula to find the area of a triangle with sides a=11, b=9,c=8. Round your answer to 4 decimal places.
A= approx 35.4965
200
Convert the given coordinates from cartesian coordinates to polar coordinates...
(6,6)
(6roots of 2, pi/4)
300
Determine the solutions in the interval [0,2pi) to the given equations...
4sin^2(x)-1=0
pi/6, 5pi/6, 7pi/6, 11pi/6
300
Find angle A, with the given sides measuring at a=125, b=115, c=60
85 degrees
300
Given the initial point (7,8) and the terminal point(11,16), write the vector v in terms of i and j.
4i+8j
300
Use the two sides and the included angle to determine the area of an oblique triangle (Round your answer to three decimal places).
Angle B=130 degree
a=62
c=20
474.948
300
Convert the given polar equation to a Cartesian equation
r= 8sin(theta)
x2+y2-8y=0
400
Solve the triangle, if possible. If there are two possible triangles, solve both (Round to two decimal places)
AngleB=35 degrees
AngleC=86 degress
Side a = 6.1
Side b=4.08
AngleA= 59 degrees
Side c= 7.1
400
Using the law of cosine, solve a triangle with the given sides of(Round your answer to three decimal places).
a=6.1
b=10.3
c=5.2
angle A=26.434 degrees
Angle B=131.263 degrees
Angle C=22.303
400
Given that u = < -4,6 >, v = < 2,11>, evaluate 3u-4v
(-20,-26)
400
To determine how far a boat is from shore, two radar stations 500 feet apart find the angles out to the boat, as shown below. Determine the distance of the boat from the shore. Round your answers to the nearest whole foot.
531 feet from shore
400
Convert the given polar equation to a polar equation
x2+y2=3y
r=3sin(theta)
500
Prove the identity...
sin(2x)=2tan(x)/1+tan^2(x)
sin(2x)
500
Find all exact solutions on the interval [0,2pi).
Cos(2x)+cos(x)=0
pi/3, 5pi/3, pi
500
A 60- pound box is resting on a ramp the is inclined 12 degrees. Rounding to the nearest tenth,
a. Find the magnitude of the normal component of the force.
b. Find the magnitude of the component of the force that is parallel to the ramp.
a. 58.7 pounds
b. 12.5 pounds
500
An airplane is heading north at a speed of 600 km/hr with wind blowing from the southwest at 80 km/hr. How many degrees off course will the plane end up flying, and what is the plane’s speed relative to the ground?
Speed=659.001
Degrees off course=4.924 degrees
500
Write the equation of the given polar graph
r=5sin5(theta)