Question

12cos²α-4sin²α, если cosα= -0.4 11sin²α-5cos²α, если sinαα= -0.4

Answer 1

first 4/25 second -61/25

Answer 2

To find the values of the given expressions, we need to substitute the given values of cosα and sinα and then perform the calculations.

Given:

• cosα = -0.4
• sinα = -0.4

We can use the trigonometric identity: sin²α + cos²α = 1 to find cos²α and sin²α:

1. sin²α = 1 - cos²α
2. sin²α = 1 - (-0.4)²
3. sin²α = 1 - 0.16
4. sin²α = 0.84

Now, we can calculate the first expression:

1. 12cos²α - 4sin²α
2. 12(-0.4)² - 4(0.84)
3. 12(0.16) - 4(0.84)
4. 1.92 - 3.36
5. -1.44

So, the value of 12cos²α - 4sin²α when cosα = -0.4 and sinα = -0.4 is -1.44.

Next, let's calculate the second expression:

1. 11sin²α - 5cos²α
2. 11(0.84) - 5(-0.4)²
3. 11(0.84) - 5(0.16)
4. 9.24 - 0.80
5. 8.44

So, the value of 11sin²α - 5cos²α when cosα = -0.4 and sinα = -0.4 is 8.44.