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Find sin x/2 , cos x/2 , and tan x/2 from the given information. sec(x) = 10/9 , 270° < x < 360°

sin x/2 =

cos x/2 =

tan x/2 =

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facundo3141592

Given that sec(x) = 10/9 and that 270° < x < 360°, we want to complete:

  • sin x/2 =  
  • cos x/2 =
  • tan x/2 =

We will find that x = 334.16°

The solutions are:

  • sin(334.16°/2) = 0.221
  • cos(334.16°/2) = -0.975
  • tan(334.16°/2) = -0.229

Remember that sec(x) = 1/cos(x)

Then:

sec(x) = 10/9 = 1/cos(x)

so we can write:

cos(x) = 9/10

If we apply the inverse cosine function, we get:

Acos(cos(x)) = Acos(9/10)

x = 25.84°

But this is not in the wanted interval, because the cosine function is even, we have that:

cos(25.84°) = cos( -25.84°)

And it has a periodicity of 360°, then:

cos(-25.84°) = cos(-25.84° + 360°)  = cos(334.16°)

Then our angle is x = 334.16°.

Now we replace that in the wanted expressions:

  • sin(334.16°/2) = 0.221
  • cos(334.16°/2) = -0.975
  • tan(334.16°/2) = -0.229

If you want to learn more, you can read:

https://brainly.com/question/15946191