Question

1)ctg(-arcsin0,6) 2)2sin(arcctg)

Answer 1

$ctg(-\arcsin0.6)=- \frac{\cos(\arcsin0.6)}{\sin(\arcsin0.6)} =- \frac{ \sqrt{1-0.6^2} }{0.6} =- \frac{0.8}{0.6} =- \frac{4}{3}$

переписываем немодифицированные множители 2 и √3 $2 \sqrt{3} \sin (arcctg \sqrt{2} )=2 \sqrt{3} \cdot \frac{ \sqrt{3} }{3} =2$

Answer 2

1. To solve the expression ctg(-arcsin(0.6)), we'll break it down step by step:

First, let's find the value of arcsin(0.6). The arcsin function gives us the angle whose sine is 0.6. So, we have:

arcsin(0.6) ≈ 0.6435 radians

Next, we have -arcsin(0.6), which is simply the negative of the previous result:

-arcsin(0.6) ≈ -0.6435 radians

Finally, we'll calculate the cotangent (ctg) of -0.6435 radians:

ctg(-0.6435) = 1/tan(-0.6435)

Since tan(-θ) = -tan(θ), we can rewrite the expression as:

ctg(-0.6435) = 1/(-tan(0.6435))

Using a scientific calculator or trigonometric tables, we find:

tan(0.6435) ≈ 0.7454

Therefore,

ctg(-0.6435) ≈ 1/(-0.7454) ≈ -1.3422

So, ctg(-arcsin(0.6)) is approximately equal to -1.3422.

2. The expression 2sin(arcctg) involves finding the sine of the arc cotangent (arcctg) of some angle. However, you haven't specified the value of the angle for which we need to evaluate the expression. Please provide the angle so I can assist you further.