Find all values of x in the interval 0 2π that satisfy the equation

Click here to see ALL problems on Trigonometry-basics Question 511618: Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separated list.) 6 sin2(x) = 3 Find all values of x in the interval [0, 2π] that satisfy the inequality. (Enter your answer using interval notation.) 3 sin(x) > 3 cos(x) Answer by lwsshak3(11628)     (Show Source): You can put this solution on YOUR website! Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separated list.) 6 sin2(x) = 3 Find all values of x in the interval [0, 2π] that satisfy the inequality. (Enter your answer using interval notation.) 3 sin(x) > 3 cos(x) ** 6 sin2(x) = 3 sin^2(x)=3/6=1/2 Sin(x)=1/√2 x=(π/4, 3π/4) (in quadrants I and II where sin>0 .. 3 sin(x) > 3 cos(x) 3 sin(x)/3 cos(x) >0 tan(x)>0 (0,π/2) U (π,3π/2) (in quadrants I and III where tan>0 Table of Contents Show Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separated list.)? 18 cos(x) - 9 = 0 What are the solutions in the interval 0 ≤ θ 2π? Does 0 2pi include 0?

Solution:

Given, the equation is 18 cos(x) - 9 = 0

We have to all values of x in the interval [0, 2π]

Now, 18 cos(x) = 9

cos(x) = 9/18

cos(x) = 1/2

We can use the unit circle to find which angles satisfy the equation.

Points on the unit circle are (cos, sin)

So, any point on the unit circle that has an x value of 1/2 is a solution.

We know,

cos(π/3) = 1/2

cos(5π/3) = 1/2

Therefore, the values of x are π/3, 5π/3.

Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separated list.)? 18 cos(x) - 9 = 0

Summary:

All the values of x in the interval [0, 2π] that satisfy the equation 18 cos(x) - 9 = 0 are π/3, 5π/3.

The trigonometric equation 10 cos(x) - 5 = 0

10 cos(x) = 5

cos (x) = 5/10

cos (x) = 1/2

cos (x) = cos (π/3)

Principal value is x = π/3

The genaral solution of cos(θ) = cos(α) is θ = 2nπ ± α, where n is an integer.

x = 2nπ ± (π/3)

If n = 0, x = 2(0)π + (π/3) and x = 2(0)π - (π/3) = π/3 and - π/3.

If n = 1, x = 2(1)π + (π/3) and x = 2(1)π - (π/3) = 2π + π/3 and 2π - π/3 = 7π/3 and 5π/3.

Therefore, the solutions of the given equation are x = π/3, x = 5π/3 and x = 7π/3 in the interval [0, 2π].

Explanation:

First isolate X:
#18cosx-9=0#
#18cosx=9#
#cosx=9/18#
#cosx=1/2#
Now that we know that Cosine of X =#1/2#, we can use the unit circle to find which angles satisty the equation.
Points on the unit circle are #(cos, sin)#, so any point on the unit circle that has an x value of #1/2# is a solution. The angles that satisfy this condition are #pi/3# and #(5pi)/3#.

What are the solutions in the interval 0 ≤ θ 2π?

Does 0 2pi include 0?