Question

1) 4cos260° + 5ctg45°

Answer 1

Ответ: 4cos(260°)+5

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Answer 2

Let's solve the expression step by step:

1. 4cos(260°):

First, we need to find the reference angle for 260° within one full rotation (360°). To do this, subtract the nearest multiple of 360° from 260°: 260° - 1 * 360° = -100°

Since cosine is positive in the fourth quadrant, we can treat the angle as positive and find the cosine value of the reference angle (100°) using the unit circle or a calculator: cos(100°) ≈ -0.1736

Now, multiply this value by 4: 4 * -0.1736 ≈ -0.6944

2. 5ctg(45°):

The cotangent (ctg) of an angle is the reciprocal of the tangent. The tangent of 45° is 1, so the cotangent of 45° is also 1.

Now, multiply this value by 5: 5 * 1 = 5

Finally, add the results from step 1 and step 2: -0.6944 + 5 ≈ 4.3056

So, 4cos(260°) + 5ctg(45°) is approximately 4.3056.