Question

Вычислите 2sin^2(п/3) и 2sin^2(3п/4)

Answer 1

2sin²(π/3)=2*(√3/2)²=2*3/4=3/2=1,5
2sin²(3π/4)=2*(√2/2)²=2*2/4=1

Answer 2

To calculate the values of the expressions 2sin^2(π/3) and 2sin^2(3π/4), you need to use trigonometric identities. Let's start with the first expression:

1. 2sin^2(π/3):

First, we need to determine the value of sin(π/3). The sine of π/3 (60 degrees) can be found using the trigonometric values for common angles. The value of sin(π/3) is √3/2.

Now, we can compute the expression:

2sin^2(π/3) = 2 * (sin(π/3))^2 = 2 * (√3/2)^2 = 2 * (3/4) = 3/2.

So, 2sin^2(π/3) = 3/2.

2. 2sin^2(3π/4):

Again, let's first find the value of sin(3π/4). The sine of 3π/4 (135 degrees) is -√2/2.

Now, we can compute the expression:

2sin^2(3π/4) = 2 * (sin(3π/4))^2 = 2 * (-√2/2)^2 = 2 * (2/4) = 2/2 = 1.

So, 2sin^2(3π/4) = 1.

To summarize:

2sin^2(π/3) = 3/2 2sin^2(3π/4) = 1