Question

Cos альфа = 1/2 Альфа принадлежит 4 степени Найти: синус альфа, тангенс альфа, катангенс альфа, cos2альфа, sin2 альфа

Answer 1

Ответ:

sin∝= - √3/2    tg ∝= -√3   ctg ∝=-√3/3    cos 2∝=-1/2         sin2∝=- √3/2

Пошаговое объяснение:

cos∝= 1/2

sin²∝+cos²∝=1

sin∝=±√1-cos²∝=±√1-1/4=±√4/4-1/4=±√3/4=±√3/2

т.к.∝∈4 четверти, то sin∝<0 ⇒ sin∝= - √3/2

tg ∝= sih∝/cos∝= - √3/2/1/2= - - √3/2*2/1= -√3

ctg ∝= - 1/√3= -√3/3

cos 2∝= cos²∝-sin²∝=1/4-3/4= - 2/4= -1/2

sin2∝= 2cos∝sin∝=2*1/2*(- √3/2)=- √3/2

Answer 2

To find the values of trigonometric functions for the given value of cos(α) = 1/2, where α belongs to the fourth quadrant (since cos(α) is positive and sin(α) is negative), we'll use the Pythagorean identity and other trigonometric identities to calculate the values:

1. We know that cos²(α) + sin²(α) = 1 (Pythagorean identity).
2. We also know that tan(α) = sin(α) / cos(α) and cot(α) = 1 / tan(α) (reciprocal identities).
3. Additionally, sin²(α) = 1 - cos²(α) (trigonometric identity).

Let's proceed with the calculations:

Given: cos(α) = 1/2

1. Sin(α): Using the Pythagorean identity: cos²(α) + sin²(α) = 1 sin²(α) = 1 - cos²(α) sin²(α) = 1 - (1/2)² sin²(α) = 1 - 1/4 sin²(α) = 3/4

Since α is in the fourth quadrant, sin(α) is negative: sin(α) = -√(3/4) = -√3/2

2. Tan(α): tan(α) = sin(α) / cos(α) tan(α) = (-√3/2) / (1/2) tan(α) = -√3

3. Cot(α): cot(α) = 1 / tan(α) cot(α) = 1 / (-√3) cot(α) = -1/√3

4. cos²(α): cos²(α) = (1/2)² cos²(α) = 1/4

5. sin²(α): We already calculated sin²(α) earlier: sin²(α) = 3/4

So, the final values are:

• Sin(α) = -√3/2
• Tan(α) = -√3
• Cot(α) = -1/√3
• cos²(α) = 1/4
• sin²(α) = 3/4