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PRE CALCULUS HELP PLEASEEEE !!!!?

+1 vote
Solve this equation. Give a general formula for all the solutions using k to represent your arbitrary integer and using only angles between 0 and 2π.
1) tan theta= -sqrt3/3
(should be two different answers)

Solve this equation on the interval 0 θ < 2π. Round your answers to two decimal places. If there is no solution, enter NONE.
2) cos(2theta) + 6 sin^2 theta= 4
(should be 4 different answers)

For each of the following, find all solutions. The variable n denotes a generic integer. (For each, select all that apply.)

3) cot^2(x)-3=0
a)none of these
b)pi/3+2pi n
c)5pi/6 + pi n
d)pi/3 + pi n
e) pi/6 + pi n
asked Feb 20, 2013 in PRECALCULUS by abstain12 Apprentice

3 Answers

+1 vote

3). cot2(x) - 3 = 0

Add 3 to each side.

cot2(x) = 3.

Take square root each side.

√[cot2(x)] = √3.

cot(x) = √3

Trigonometric table in cot(30°) = √3

cot(x) = cot(30°)

x = 30°= π/6

Therefore x = π/6 + nπ where n is an integer.

Option e is right choice.

answered Feb 20, 2013 by richardson Scholar
+1 vote

1) tan(θ) = -√3/3

This expression it can be written as tan(θ) = -[√3/(√3)(√3)]

So, tan(θ) = -1/√3

Trigonometric table in tan(180 - 30) = -1/√3 or tan(360 - 30) = -1/√3

i.e. tan(150°) = -1/√3 or tan(330°) = -1/√3

tan(θ) = tan(150°) or tan(θ) = tan(330°)

θ = 150° = 5π/6 + nπ or 330°= 11π/6 + nπ

Therefore θ = 5π/6 + nπ or 11π/6 + nπ.

answered Feb 20, 2013 by richardson Scholar
0 votes

2) The trigonometric equation image

image

image

image

image

image

image

image

image

The general solution of image where is an integer.

image

image

image or image

The solutions outside the interval [0, 2π ) are

If n = 0 then image

If n = 2 then image

The solutions in the interval [0, 2π) are

image

image

image

image

The solutions in the interval [0, 2π) are π/3, 2π/3, 4π/3 and 5π/3.

answered Jun 23, 2014 by david Expert

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