Given sin x=2/3, find the exact value of sin(2x), where x is a first quadrant angle.?

Question

I'm not asking you to solve it for me, I just wanted to ask if you're suppose to do this with a calculator, or you can do it without one. Because if you use a calculator it'd be super easy, whereas without me a bit tough

Answer 1

You can use it with out a calculator.

first make a right triangle such that sin x = 2/3

Use the pythagorean theorem to find the missing side

Find cos x

then plug it into sin 2x = 2sinxcosx

Answer 2

sketch the right triangle, hypotenuse 3, vertical side 2 (so sin x = 2/3), horizontal side √5 (3² - 2² = 5). so cos x = √5 / 3.

then using double angle formula,
sin(2x) = 2 sin x cos x = 2 • 2/3 • √5/3 = 4√5 / 3.

Answer 3

You should be able to do it with or without a calculator. Use the formula sin(2x) = 2sin x cos x.

cos x can be found using sin^2 x + cos^2 x = 1

Answer 4

Yes. Just put 2/3 and hit the "sin -1" button. If you want to get the doble angle, multiply what you got by 2.

Answer 5

sin(2x)
= 2sin(x)cos(x)
= 2(2/3)(√5 / 3)
= 4√5 / 9
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Ideas: Use a right triangle with sides 2-√5-3.

Answer 6

sin(2x) = 2sin(x)cos(x)

Since sine of x = 2/3 cosine of x can be found using the Pythagorean theorem. 3^2 = 2^2 + n^2; n = sqrt(5), so cos(x) = sqrt(5)/3

Answer 7

sin 2x = 2 sin x cos x
. . . . .. = 2 ( 2/3 ) ( sqr(5) / 3 )
. . . . .. = 4 sqr(5) / 9

Answer 8

Uh.... I'm only in the eighth grade! my brain hurts!