Question

Ctg a = -3/4 і п/2 знайти tg a? sin a? cos a?

Answer 1

Смотри решение на фото

Answer 2

To find the values of tg a (tangent), sin a (sine), and cos a (cosine) for the angle a = -3/4 * π/2, we can proceed as follows:

First, let's clarify the value of a: a = -3/4 * π/2 = -(3/4) * (π/2) = -3π/8

Now, let's find the values:

1. Tangent (tg a): Tangent is defined as the ratio of sine to cosine. tg a = sin a / cos a

2. Sine (sin a): The sine of an angle is the y-coordinate of the point on the unit circle corresponding to that angle. sin a = sin(-3π/8)

3. Cosine (cos a): The cosine of an angle is the x-coordinate of the point on the unit circle corresponding to that angle. cos a = cos(-3π/8)

Now, we'll calculate each value:

Step 1: Calculate sin(-3π/8) and cos(-3π/8): We can use the trigonometric values of common angles to calculate these values: sin(-π/4) = -√2/2 cos(-π/4) = √2/2

Step 2: Convert sin(-π/4) and cos(-π/4) to sin(-3π/8) and cos(-3π/8): Using the trigonometric angle sum/difference formulas: sin(-3π/8) = sin(-π/4) = -√2/2 cos(-3π/8) = cos(-π/4) = √2/2

Now, we have all the values:

1. Tangent (tg a): tg a = sin a / cos a = (-√2/2) / (√2/2) = -√2

2. Sine (sin a): sin a = sin(-3π/8) = -√2/2

3. Cosine (cos a): cos a = cos(-3π/8) = √2/2

So, the values are: tg a = -√2 sin a = -√2/2 cos a = √2/2