Question

1) Найдите tgA, если (7sinA - 2cosA)/(4sinA - 9cosA) = 2 2) Найдите sin (7п/2 - A), если sinA = 0,8 и A принадлежит (п/2;п) Распишите все решение, пожалуйста

Answer 1

Применены: определение тангенса,  формулы приведения, формула зависимости косинуса от синуса

Answer 2

Finding tgA:

To find the value of tgA, we can use the given equation:

(7sinA - 2cosA)/(4sinA - 9cosA) = 2

To simplify the equation, we can multiply both the numerator and denominator by cosA:

(7sinA - 2cosA)/(4sinA - 9cosA) * (cosA/cosA) = 2

Simplifying further, we get:

(7sinA * cosA - 2cos^2A)/(4sinA * cosA - 9cos^2A) = 2

Using the trigonometric identity sin^2A + cos^2A = 1, we can substitute sin^2A with (1 - cos^2A):

(7sinA * cosA - 2(1 - sin^2A))/(4sinA * cosA - 9(1 - sin^2A)) = 2

Expanding and simplifying, we have:

(7sinA * cosA - 2 + 2sin^2A)/(4sinA * cosA - 9 + 9sin^2A) = 2

Rearranging the terms, we get:

(2sin^2A + 7sinA * cosA - 2)/(9sin^2A + 4sinA * cosA - 9) = 2

Now, let's solve this equation to find the value of tgA.

Note: To find the exact value of tgA, we need additional information about the values of sinA and cosA. Please provide the values of sinA and cosA so that we can proceed with the calculation.

Finding sin(7π/2 + A):

To find the value of sin(7π/2 + A), we can use the given equation:

sinA = 0.8

We know that sin(π/2 + A) = cosA. Therefore, we can rewrite the equation as:

cos(π/2 + A) = 0.8

Using the trigonometric identity cos(π/2 + A) = -sinA, we can substitute -sinA for cos(π/2 + A):

-sinA = 0.8

Solving for sinA, we get:

sinA = -0.8

Now, let's find the value of sin(7π/2 + A) using the given value of sinA.

sin(7π/2 + A) = sin(3π/2 + 2π + A)

Since sin(3π/2) = -1, we can rewrite the equation as:

sin(7π/2 + A) = -sinA

Substituting the value of sinA, we have:

sin(7π/2 + A) = -(-0.8)

Simplifying, we get:

sin(7π/2 + A) = 0.8

Therefore, the value of sin(7π/2 + A) is 0.8.

Summary:

1) To find tgA, we need additional information about the values of sinA and cosA. Please provide the values of sinA and cosA so that we can proceed with the calculation. 2) Given sinA = 0.8, we can find sin(7π/2 + A) = 0.8.