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Given sin x =-4/5 and x is in quadrent 3, what is the value of tan x/2

4vir4ik [10]

Answer:

We can write sin x in terms of tan x/2 using the formula:

⇒ sin x = (2 tan (x/2)) / (1 + tan2(x/2))

Therefore, using the above formula, we can find the values of tan x/2 by putting the value of sin x.

⇒ -4/5 = (2 tan (x/2)) / (1 + tan2(x/2))

Now, if we replace tan (x/2) by y, we get a quadratic equation:

⇒ 0.8y2 + 2y + 0.8 = 0

⇒ 2y2 + 5y + 2 = 0

By using the quadratic formula, we get y = -0.5, -2

Hence, the value of tan (x/2) = -0.5, -2

Now, we have two solutions of tan (x/2).

Now, let's check for the ideal solution using the formula tan x = (2 tan (x/2)) / (1 - tan2(x/2)).

For tan (x/2) = -0.5:

⇒ tan x = 2(-0.5) / 1 - (-0.5)2 = -4/3

It is also given that x lies in the third quadrant. We know that tan is positive in the third quadrant, and here we get tan x = -4/3 which is negative.

Hence, we can say that tan (x/2) = -0.5 is not a correct solution. Hence it is rejected.

Now let's check for tan (x/2) = -2.

⇒ tan x = 2(-2) / 1 - (-2)2 = 4/3

Here, we get tan x = 4/3 which is positive.

Hence, we can say that tan (x/2) = -2 is a correct solution.

5 0

3 years ago

It takes 20 minutes to make 4 model airplanes. How many model airplanes can be made in 2 hours?

Viefleur [7K]

Answer: 24 model airplanes can be made in 2 hours.

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Help me find the range of this function please

lara31 [8.8K]

Answer:

{-2, -14, -26, -50}

Step-by-step explanation:

The range of the function is the function evaluated at each point of the given domain. So to find the range of the function we need to find the value of the function for each point in the domain:

- For x = -8

$f(x)=-2x-18$