Question

Сравните tg(-84°) и ctg175°

Answer 1

Решение задания смотри на фотографии

Answer 2

To compare the values of tangent and cotangent functions, we need to first find their respective numerical values. Keep in mind that trigonometric functions are periodic, so we can use their periodicity to find equivalent angles within one period (360 degrees or 2π radians).

1. Finding tg(-84°): Since the tangent function is periodic with a period of 180 degrees, we can find an equivalent angle within the first period: -84° + 180° = 96°

Now, we need to determine the value of tangent for the angle 96°. However, it's important to note that tangent is an odd function: tg(-θ) = -tg(θ)

So, tg(-84°) = -tg(96°)

2. Finding ctg(175°): Since the cotangent function is the reciprocal of the tangent function, we can use the result from step 1 to find an equivalent angle for ctg(175°): 175° + 180° = 355°

Now, we need to determine the value of cotangent for the angle 355°.

So, ctg(175°) = ctg(355°)

To proceed, we should know the quadrant in which the angle 355° lies. In the unit circle, this angle is in the fourth quadrant. In the fourth quadrant, both sine and cosine are positive.

For an angle θ in the fourth quadrant: ctg(θ) = 1 / tg(θ)

From step 1, we know that: tg(96°) = -tg(-84°)

Therefore: ctg(175°) = 1 / (-tg(-84°))

Now, we need to evaluate tg(-84°) to find ctg(175°).

For reference, the tangent function is defined as: tg(θ) = sin(θ) / cos(θ)

You would need a calculator to determine the specific numerical values of tg(-84°) and ctg(175°) as they involve trigonometric computations.