Question

А)cos(-4П:3) б)tg(-13П:6) помогите решить пажалуйста

Answer 1

Первое - табличный результат.
а) и минус можно убрать, потому что функция четная. 
$cos( \frac{4 \pi }{3} )=- \frac{1}{2}$
б) И у тангенса можно отбрасывать полный период. он у него составляет просто $\pi$. Минус выносится перед функцией:
$-tg( \frac{ \pi }{6})= \frac{ \sqrt{3} }{3}$
вот и все

Answer 2

Calculating Trigonometric Functions

To solve the given trigonometric expressions, we can use the unit circle or a calculator. Let's calculate each expression step by step.

a) cos(-4π/3):

To find the value of cos(-4π/3), we need to determine the angle on the unit circle that corresponds to -4π/3 radians.

The unit circle is a circle with a radius of 1, centered at the origin of a coordinate plane. The angle is measured counterclockwise from the positive x-axis.

To convert -4π/3 radians to degrees, we can use the conversion factor: 180 degrees = π radians.

-4π/3 radians = (-4π/3) * (180 degrees/π radians) = -240 degrees.

Since cosine is a periodic function with a period of 360 degrees, we can add or subtract multiples of 360 degrees to the angle without changing the value of the cosine function.

-240 degrees + 360 degrees = 120 degrees.

Now, we need to find the cosine of 120 degrees. Using a calculator or trigonometric table, we find that cos(120 degrees) = -0.5.

Therefore, cos(-4π/3) = -0.5.

b) tg(-13π/6):

To find the value of tg(-13π/6), we need to determine the angle on the unit circle that corresponds to -13π/6 radians.

Using the same conversion factor as before, we can convert -13π/6 radians to degrees:

-13π/6 radians = (-13π/6) * (180 degrees/π radians) = -390 degrees.

Again, since the tangent function is periodic with a period of 180 degrees, we can add or subtract multiples of 180 degrees to the angle without changing the value of the tangent function.

-390 degrees + 180 degrees = -210 degrees.

Now, we need to find the tangent of -210 degrees. Using a calculator or trigonometric table, we find that tg(-210 degrees) = 1.

Therefore, tg(-13π/6) = 1.

To summarize: a) cos(-4π/3) = -0.5 b) tg(-13π/6) = 1

I hope this helps! Let me know if you have any further questions.