Question

find value of sin 2090​

Answer 1

Step-by-step explanation:

i am not getting it please explain the question

Answer 2

Step-by-step explanation:

You should be able to find it using the trig identity: sin(3x)=3sin(x)−4sin3(x)

(I assume this is derived from the identity: sin(x+y) = sin(x)cos(y) + cos(x)sin(y), but used twice. To be honest, I just looked it up.)

Now that we know this, make x=20.

sin(60)=3sin(20)−4sin3(20)

Then make two substitutions. sin(60)=3√2 and y = sin(20)

3√2=3y−4y3

And then with some manipulation:

y3−34y+3√8=0

All that remains is to solve for y. Solving cubics by hand is a pain, but I will point you here: How can I solve an equation of the third degree? Then I will wave my hands around a bit and solve it here: Computational Knowledge Engine

You get 3 solutions. One negative (not correct) the other two are approximately .34 and .64.

Which one is it? sin(30) =.5, and because we know the sine function is increasing up to 90 degrees the solution is approximately .34.

So, what is the exact solution? According to Wolfram Alpha:

This should yield a real number, but I’m not about to simplify that mess for you.

Suffice to say, it can be done, but it’s unsurprisingly a huge headache.