Trigonometric
Identities
Identities
Use the sum and difference formulas for sine to solve, sin(135-120)
Simplify to Sq6-Sq2/4.
Find the x and y components of a vector at an angle of 60 degrees from the point of origin and a magnitude of 8.
<4, 4Sq3>
Using Heron’s formula = a+b+c/2 determine the area of a triangle where the sides are 6, 8, and 12.
Area = 13
What of the polar coordinates below reference the same point (6, pi/6):
A. (-6, -pi/6) B. (-6, -5pi/6)
C. (6, -11pi/6) D. (-6, 11pi/6)
B and C
What is the simplified version of 2(1-sin2(x))-1?
Cos(2x)
Verify the identity, cot x * sec x * sin x=1
Simplify to, (cos x/ sin x) * (1/ cos x) * sin x=1
Find the magnitude and direction of the vector, v=6i-6j
Magnitude is 6Sq2
Direction= -45 degrees
Find the area of a triangle when given two sides and one angle, <C= 24, a=21, b=16
Area= 68.33
Convert these cartesian coordinates rounded to two decimals: (6, pi/6)
(5.20,3)
Determine the magnitude and direction of a vector with an initial point P (2,13) and a terminal point Q (-4,9)
Magnitude: 2Sq13
Direction: tan^-1(-4,-6)=tan^-1(2/3)
Given theta= -3/4 and is in Quadrant 2, determine tan(2Theta)
-24/7
If a+b then find the magnitude.
a= <2,-3,5>
b= <-2,6,-1>
Magnitude = 5
Use the law of sines to solve the triangle with <A=24, a=8.5, and c=10.6.
<C=30.5, <B=125.5, b=17
What are these cartesian coordinates converted to polar coordinates rounded to one decimal, (7, 60°)
(3.5, 6.1)
A pendulum swings one complete swing every 5 seconds at a maximum angle of 14 degrees. Determine an equation of the angle as a function of time (t).
Theta(t)= 14sin (2pi/5 t)
Use Pythagorean identities to verify csc x/ sin x - cot x/ tan x
Simplify to sin^2(x)/sin^2(x) =1
Sketch the graph f(x)= 1/x-2 an state any asymptote.
X=2, y=0
Determine the amount of triangles possible with the angle A= 20 and sides a=7 and b=10
There are two solutions and two triangles.
Find the equation for the polar graph
R= 1+1cos(theta)
Determine the solutions on the interval [0, 2pi) for 2sin(2x)-1=0
Pi/12, 5pi/12, 13pi/12, 17pi/12
Find all solutions to the trigonometric equation, cos theta = 1/2
Theta= pi/3 +/- 2kpi and Theta= 5pi/3 +/- 2kpi
Find U + V and U - V, if U=<3,4> and V=<5,-1>
U+V= <8,3>
U-V= <-2,5>
Use the law of sines and the law of cosines to solve the triangle given the following, <C=98, a=8, b=5.
c= 10
<A= 54.2
<B=29.6
Find the equation based on the polar graph.
r= 6 cos(2theta)
Determine the solutions on the interval [0, 2pi) given sin^2(x)-5sin(x)-6=0
3pi/2