Question

-12/Sin^2 131+sin^2 221

Answer 1

Решается с помощью формул приведения.
180°=2π, значит, не меняем на косинус.
270°=3π/2, значит, меняем на косинус.
т.к. синус в квадрате, то знак в любом случае будет +

Answer 2

To simplify the expression, we'll start by evaluating each part separately:

1. Evaluating -12 / Sin^2(131): The "^" symbol typically denotes exponentiation, but it seems like a typo or misunderstanding here. I assume you meant to write "-12 / Sin(131)^2". To calculate this, we first find the value of Sin(131) and then square it.

Note: Trigonometric functions typically take angles in degrees, not radians, so I'll assume the angles are in degrees.

a. Sin(131): Sin(131 degrees) ≈ 0.8746

b. Sin(131)^2: Sin(131 degrees)^2 ≈ 0.8746^2 ≈ 0.7644

2. Evaluating Sin^2(221): a. Sin(221): Sin(221 degrees) ≈ -0.9998

b. Sin(221)^2: Sin(221 degrees)^2 ≈ (-0.9998)^2 ≈ 0.9996

Now, let's put the two parts back into the expression and solve it:

Expression: -12 / Sin^2(131) + Sin^2(221)

Substituting the calculated values:

-12 / 0.7644 + 0.9996

Now, calculate each part:

a. -12 / 0.7644 ≈ -15.6853 b. 0.9996

Finally, add the two parts:

-15.6853 + 0.9996 ≈ -14.6857

So, the simplified value of the expression is approximately -14.6857.