Find the measure of a negative angle coterminal with 4л 3 radians.

Mathematics

1 answer:

bearhunter [10]1 year ago

4 0

we can conclude that the measure of a negative angle coterminal with 4л/3 is B = -2л/3

<h3>How to find the coterminal angle?</h3>

For a given angle A, we define the family of coterminal angles as:

B = A + n*2л

Where n is an integer number.

In this case, we want to find a negative coterminal angle to A = (4л/3), then we can replace it in the above formula to get:

B = 4л/3 + n*2л

Now we just need to find a value of n such that B is negative, if we select n = -1, then:

B = 4л/3 - 2л = 4л/3 - 6л/3 = -2л/3

Then we can conclude that the measure of a negative angle coterminal with 4л/3 is B = -2л/3.

If you want to learn more about coterminal angles:

brainly.com/question/3286526

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PLEASE HELP! I'll give 5 out of 5 stars, give thanks, and give as many points as I can.

Liula [17]

Answer:

$\boxed{\boxed{x=\dfrac{\pi}{3}\ \vee\ x=\pi\ \vee\ x=\dfrac{5\pi}{3}}}$

Step-by-step explanation:

$\cos(3x)=-1\iff3x=\pi+2k\pi\qquad k\in\mathbb{Z}\\\\\text{divide both sides by 3}\\\\x=\dfrac{\pi}{3}+\dfrac{2k\pi}{3}\\\\x\in[0,\ 2\pi)$

$\text{for}\ k=0\to x=\dfrac{\pi}{3}+\dfrac{2(0)\pi}{3}=\dfrac{\pi}{3}+0=\boxed{\dfrac{\pi}{3}}\in[0,\ 2\pi)\\\\\text{for}\ k=1\to x=\dfrac{\pi}{3}+\dfrac{2(1)\pi}{3}=\dfrac{\pi}{3}+\dfrac{2\pi}{3}=\dfrac{3\pi}{3}=\boxed{\pi}\in[0,\ 2\pi)\\\\\text{for}\ k=2\to x=\dfrac{\pi}{3}+\dfrac{2(2)\pi}{3}=\dfrac{\pi}{3}+\dfrac{4\pi}{3}=\boxed{\dfrac{5\pi}{3}}\in[0,\ 2\pi)\\\\\text{for}\ k=3\to x=\dfrac{\pi}{3}+\dfrac{2(3)\pi}{3}=\dfrac{\pi}{3}+\dfrac{6\pi}{3}=\dfrac{7\pi}{3}\notin[0,\ 2\po)$