Trigonometry Answers

cos2x=1/2 interval (0, pi) solve the equation

how to find all solutions of cos(x)= sin(x) in the interval [0,2(3.14))

Prove that : tanA + tan(A + π/3) + tan(A + 2π/3) = 3

sin(x) is an odd function and cos(x) is an even function.
a) Define f(x) as a modification of sin(x) so that f is even.
b) Define g(x) as a modification of cos(x) so that g is odd.

In the following, perform the graphing on some electronic gadget
– not here. When you describe what you see. Words like “peak”, “valley”,
and asymptote might be useful.
a) Graph sec(x) and cos(x) together. Describe how the two graphs interact.
b) Graph 2*sec(x) and 2*cos(x) together. Describe how the two graphs
interact.
c) Graph sec(2x) and cos(2x) together. Describe how the two graphs interact.

Start with g(x) = sin(x).
Hint: Make sure you got the correct function by graphing it on some electronic gadget.
a) Define gA(x) to change the amplitude of g to 2.
b) Define gB(x) to change the amplitude of g to 1/2.
c) Define gC(x) to change the period to π.
d) Define gD(x) to change the period to 4π

Start with f(x) = cos(x).
Hint: Make sure you got the correct function by graphing it on some electronic gadget.
a) Define fA(x) so that cos is translated up by 2.
b) Define fB(x) so that cos is translated down by 2.
c) Define fC(x) so that cos is translated right by π.
d) Define fD(x) so that cos is translated left by π.

The Simpson method for angular speed is not radians per second.
It is degrees per second: ωD=r⋅D (ωD is known as Doh-mega).
In order to communicate effectively with his coworkers, Homer needs to
convert from Doh-mega to ω and from ω to Doh-mega.
(a) Write a formula to convert measurements in degrees per second (ωD) to
radians per second (ω).
(b) Write a formula to convert measurements in radians per second (ω) to
degrees per second (ωD).

Data stored on a CD is read from inner radius to outer radius. The
nominal inner radius of readable recording is 25 mm and usable recording
ends at a radius of 59 mm. On a particular player, ω = 66.0 (radians/sec).
(a) What is the linear speed under the optical pick-up at the inner radius?
(b) What is the linear speed under the optical pick-up at the outer radius?
(c) Compare the two linear speeds and make a rough rule about speeds at the
inner and outer radii?

A circle with radius of 63,010 μm is centered at the origin of a
CCS. Angles α and β are in standard position, α = 1.100 radians, and β =
1.257 radians.
a) What is the length of the arc that is captured between α and β?
b) To the nearest degree, what is the size of the angle between the terminal
side of α and the terminal side of β?
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