Question

СРООЧНО a) sin5π/4 б) tg7π/6 в)cosπ/6-ctgπ/4 г)tg3π/4cos3π/4+ctg(-π/6)sinπ/6 д)sin510градусов-sin270град.ctg270град. упростить cos^2t-sin^2t/tg(-t)ctgt

Answer 1

Решение смотри на фотографии

Answer 2

a) sin(5π/4)

To find the value of sin(5π/4), we can use the unit circle or a calculator. The sine function represents the y-coordinate of a point on the unit circle.

Using the unit circle, we can see that the angle 5π/4 is in the third quadrant, where the sine function is negative. Therefore, sin(5π/4) is equal to -√2/2.

б) tg(7π/6)

To find the value of tg(7π/6), we can use the tangent function. The tangent function represents the ratio of the sine and cosine functions.

Using the unit circle, we can see that the angle 7π/6 is in the third quadrant, where both the sine and cosine functions are negative. Therefore, tg(7π/6) is equal to √3.

в) cos(π/6) - ctg(π/4)

To find the value of cos(π/6) - ctg(π/4), we can use the cosine and cotangent functions.

Using the unit circle, we can see that cos(π/6) is equal to √3/2.

The cotangent function is the reciprocal of the tangent function. Since tg(π/4) is equal to 1, ctg(π/4) is also equal to 1. Therefore, ctg(π/4) is equal to 1.

So, cos(π/6) - ctg(π/4) is equal to √3/2 - 1.

г) tg(3π/4)cos(3π/4) + ctg(-π/6)sin(π/6)

To find the value of tg(3π/4)cos(3π/4) + ctg(-π/6)sin(π/6), we can use the tangent and cotangent functions, as well as the cosine and sine functions.

Using the unit circle, we can see that tg(3π/4) is equal to 1, cos(3π/4) is equal to -√2/2, ctg(-π/6) is equal to -√3, and sin(π/6) is equal to 1/2.

Therefore, tg(3π/4)cos(3π/4) + ctg(-π/6)sin(π/6) is equal to 1 * (-√2/2) + (-√3) * (1/2).

д) sin(510 degrees) - sin(270 degrees) * ctg(270 degrees)

To find the value of sin(510 degrees) - sin(270 degrees) * ctg(270 degrees), we can use the sine and cotangent functions.

Using the unit circle, we can see that sin(510 degrees) is equal to -1/2, sin(270 degrees) is equal to -1, and ctg(270 degrees) is equal to 0.

Therefore, sin(510 degrees) - sin(270 degrees) * ctg(270 degrees) is equal to -1/2 - (-1) * 0.

упростить cos^2(t) - sin^2(t) / tg(-t) * ctg(t)

To simplify cos^2(t) - sin^2(t) / tg(-t) * ctg(t), we can use the trigonometric identities.

The identity cos^2(t) - sin^2(t) is equal to cos(2t).

The identity tg(-t) * ctg(t) is equal to -1.

Therefore, cos^2(t) - sin^2(t) / tg(-t) * ctg(t) simplifies to cos(2t) / -1, which is equal to -cos(2t).

Please note that the simplification assumes that the denominator is not equal to zero.