Question

5sin²64°+6cos60°+5cos²64°

Answer 1

5sin²64°+6cos60°+5cos²64° = (5sin²64°+ 5cos²64°) +6cos60° =
5(sin²64°+ cos²64°) + 6 · 0,5 = 5 · 1 + 3 = 8

Answer 2

To simplify the given expression, we'll use trigonometric identities and basic trigonometric values.

Recall the trigonometric identities:

1. sin²θ + cos²θ = 1
2. sin(90° - θ) = cosθ
3. cos(90° - θ) = sinθ

Let's start by evaluating each term step by step:

1. 5sin²64°: Using the identity sin²θ + cos²θ = 1, we can rewrite sin²64° as 1 - cos²64°: 5sin²64° = 5(1 - cos²64°)

2. 5cos²64°: This is already in the desired form.

3. 6cos60°: cos(60°) = 1/2 6cos60° = 6 * (1/2) = 3

Now, we can put all the terms back together:

5sin²64° + 6cos60° + 5cos²64° = 5(1 - cos²64°) + 3 + 5cos²64°

Now, we need to evaluate cos²64°. For this, we use the identity cos(90° - θ) = sinθ: cos(90° - 64°) = sin(64°)

To find sin(64°), you can use a calculator or lookup in a trigonometric table. For the sake of calculation, let's assume sin(64°) ≈ 0.8988.

Now, replace cos²64° with sin²64°:

5sin²64° + 6cos60° + 5cos²64° = 5(1 - sin²64°) + 3 + 5sin²64°

Substitute the value of sin(64°):

5(1 - 0.8988²) + 3 + 5(0.8988²) ≈ 5(1 - 0.8086) + 3 + 5(0.8086) ≈ 5(0.1914) + 3 + 4.043 ≈ 0.957 + 3 + 4.043 ≈ 8.000

So, the simplified expression is approximately 8.