10th Grade - Trigonometry

10th Grade lesson

10 - Trigonometry


First, here are two formulas that you have to know by heart (or save them in your calculator !).

trigonometry formulas cosine sum
trigonometry formulas sine sum

You can find two similar formulas by replacing b by -b. But let's replace b by a in the first one. Because trigonometry formulas, we obtain trigonometry formulas and hence :
trigonometry formulas
trigonometry formulas

It's a new formula, you can do the same with sine. There are a lot of formulas in trigonometry and a lot of them are useless ! Remember these ones above.

Polar coordinates

In a frame there are two ways to locate a point : by projecting it on the x axis and on the y axis and giving the distances from point O to every projection (cartesian coordinates), or by giving the distance from point O and the angle formed with the line (OM) and the horizontal axis: these are polar coordinates.
system of polar coordinates
the cartesian coordinates of M are a and b.
the polar coordinates of M are r and teta.
To switch from a system to the other, you notice that in the triangle OMN, right-angled at N, we have, according to Pythagoras' theorem polar coordinates, and thanks to trigonometry,
polar coordinates calculation

These formulas enable us to switch from cartesian coordinates to polar coordinates. To switch from polar coordinates to cartesian ones, you just have to inverse the last two formulas : math and math.

See also : trigonometry on

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10th Grade Trigonometry

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