Question

Sin 26° - cos 26° * ctg 122°

Answer 1

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Answer 2

To solve the expression, first, we need to find the values of the trigonometric functions for the given angles:

1. sin 26°
2. cos 26°
3. ctg 122° (cotangent of 122°)

Let's start by calculating each trigonometric value step by step:

1. sin 26°: To find the sine of 26°, you can use a calculator or trigonometric tables. For simplicity, I'll provide you with the rounded value: sin 26° ≈ 0.43837.

2. cos 26°: Similarly, the cosine of 26° can be found using a calculator or trigonometric tables. The rounded value is: cos 26° ≈ 0.8988.

3. ctg 122° (cotangent of 122°): The cotangent (cot) of an angle is the reciprocal of the tangent (tan) of that angle. So, we first need to find the tangent of 122° and then take its reciprocal.

tan 122° ≈ -1.92718 (rounded)

ctg 122° = 1 / tan 122° ≈ -0.51915 (rounded)

Now that we have all the values, let's calculate the expression:

Sin 26° - cos 26° * ctg 122°

Substitute the values:

0.43837 - (0.8988 * (-0.51915))

Now perform the multiplication inside the parentheses:

0.43837 + 0.46684

Finally, sum the two values:

Result ≈ 0.90521

So, Sin 26° - cos 26° * ctg 122° ≈ 0.90521.