Find sin(2x), cos(2x), and tan(2x) from the given information. sin(x) = 3/5 , x in quadrant I

Solution:

Given, sin(x) = 3/5

We have to find the value of sin(2x), cos(2x), and tan(2x) in the first quadrant.

Let us use the know trigonometric identities to solve the given functions.

We know, sin²x + cos²x = 1

(3/5)² + cos²x = 1

cos²x = 1 - (9/25)

cos²x = 16/25

Taking square root,

cos x = ±4/5

In the first quadrant cos x has to be positive.

Thus, cos x = +4/5

Now, sin 2x = 2 sinx cosx

sin 2x = 2(3/5)(4/5)

sin 2x = 24/25

We know, cos 2x = cos²x - sin²x

cos 2x = (4/5)² - (3/5)²

cos 2x = (16/25) - (9/25)

cos 2x = (16 - 9)/25

cos 2x = 7/25

We know, tan 2x = sin 2x/cos 2x

tan 2x = (24/25)/(7/25)

tan 2x = 24/7

Therefore, the values of sin 2x, cos 2x and tan 2x are 24/25, 7/25 and 24/7.

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Find sin(2x), cos(2x), and tan(2x) from the given information. sin(x) = 3/5 , x in quadrant I

Summary:

From the given information. sin(x) = 3/5 , x in quadrant I, the values of sin 2x, cos 2x and tan 2x are 24/25, 7/25 and 24/7.