Question

Вариант 11. ВЫЧИСЛите:a) sin (-150°); cos( -240); tg (-135°); ctg 315°;​

Answer 1

$- \frac{1}{2} \\ \frac{1}{2} \\ 1 \\ - 1$

Answer 2

To calculate the trigonometric functions for the given angles, we can use the following formulas:

1. For sine (sin):

   sin(-θ) = -sin(θ)

2. For cosine (cos):

   cos(-θ) = cos(θ)

3. For tangent (tan):

   tan(-θ) = -tan(θ)

4. For cotangent (cot):

   cot(θ) = 1 / tan(θ)

Let's calculate each trigonometric function:

a) sin(-150°):

Using the formula sin(-θ) = -sin(θ): sin(-150°) = -sin(150°)

b) cos(-240°):

Using the formula cos(-θ) = cos(θ): cos(-240°) = cos(240°)

c) tan(-135°):

Using the formula tan(-θ) = -tan(θ): tan(-135°) = -tan(135°)

d) ctg(315°):

Using the formula cot(θ) = 1 / tan(θ): ctg(315°) = 1 / tan(315°)

Now, let's calculate each value:

a) sin(-150°) = -sin(150°) = -0.5

b) cos(-240°) = cos(240°) = -0.5

c) tan(-135°) = -tan(135°) = -1

d) ctg(315°) = 1 / tan(315°)

To calculate ctg(315°), we need to calculate tan(315°) first. The angle 315° lies in the fourth quadrant, and the tangent function is negative in the fourth quadrant. To find the value of tan(315°), we can use the fact that tan(315°) is equal to the tangent of its reference angle (45°) with the negative sign:

tan(315°) = -tan(45°) = -1

Now, we can find ctg(315°):

ctg(315°) = 1 / (-1) = -1

So, the final values are: a) sin(-150°) = -0.5 b) cos(-240°) = -0.5 c) tan(-135°) = -1 d) ctg(315°) = -1