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lana [24]
2 years ago
7

Can someone explain to me why are we adding 2kpi when we are doing zeros for sin and cos, but adding kpi when doing zeros for tg

? ​

Mathematics
1 answer:
makvit [3.9K]2 years ago
8 0

on the first exercise, you got a solution angle of π/18, that's a good solution for the I Quadrant only, however, on a circle, we have angles that go from 0 to 2π, however we can always keep on going around and continute to 2π + π/2 or 3π or 4π, or 115π/3 or 1,000,000π/18 and so on, and we're really just going around the circle many times over, getting a larger and larger angle, same circular motion.

π/18 on that exercise works for the I Quadrant, however if we continue and go around say 2π, we'll find that 2π/3 + π/18 is a coterminal angle with π/18, and thus that angle has also the same sine value.

π/18 + 2kπ/3 , where k = integer, is a way to say, all angles around the circle that look like this have the same sine, namely

π/18 + 2(1)π/3

π/18 + 2(2)π/3

π/18 + 2(3)π/3

π/18 + 2(5)π/3

π/18 + 2(99999999)π/3

.....

so using the "k" as some sequence multiplier, is a generic notational way to say, "all these angles".

you'll also find that "n" is used as well for the same notation, say for example

2π/3  + 2πn.

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The value of x is 81

Step-by-step explanation:

The sum of the interior angles of any quadrilateral is 360°

  • The measure of ∠1 is 40% of the sum of the angle measures of the quadrilateral
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∵ The figure have 4 sides

∴ The figure is a quadrilateral

∵ The sum of the measures of the interior angles of a

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- Add the four angles and equate the sum by 360

∴ m∠1 + m∠2 + m∠3 + x = 360

∵ m∠1 = 40% of the sum of the angle measures of the quadrilateral

∴ m∠1 = 40% × 360 = \frac{40}{100} × 360 = 144°

∵ m∠2 = 12.5% of the sum of the angle measures of the quadrilateral

∴ m∠2 = 12.5% × 360 = \frac{12.5}{100} × 360 = 45°

∵ m∠3 = 25% of the sum of the angle measures of the quadrilateral

∴ m∠3 = 25% × 360 = \frac{25}{100} × 360 = 90°

- Substitute these values in the equation above

∴ 144 + 45 + 90 + x = 360

- Add the like terms in the left hand side

∴ 279 + x = 360

- Subtract 279 from both sides

∴ x = 81°

The value of x is 81

Learn more:

You can learn more about the polygons in brainly.com/question/6281564

#LearnwithBrainly

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