Trigonometry Homework

So, if our angle was at the blank angle, then the adjacent and opposite sides above would switch. Yes, trigonometry is all about the ratios between the sides.

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Suppose a right triangle has an angle θ for one of the acute angles.

The sine of θ (sin θ) is the ratio of the opposite side to the hypotenuse, the cosine of θ (cos θ) is the ratio of the adjacent side to the hypotenuse, and the tangent of θ (tan θ) is the ratio of the opposite side to the adjacent side.

Trigonometry is where you apply your knowledge of triangles from geometry and use the resulting formulas to help you solve problems.

Many math symbols come from the Greek language and, not surprisingly, the word trigonometry also has its roots in that language.

What's so special about the right triangle, you say? The hypotenuse is always the side across from the right angle; however, the other two sides switch depending on which angle you are referring to.

Well, just looking at it, we see that a right triangle has names for all three sides. You see, the adjacent side, as the name suggests, is always next to the angle.

They are the 45-45-90 triangle (also known as the π/4, π/4, and π/2 in radian measure), and the 30-60-90 triangle (also known as π/6, π/4, and π/2).

They can be used to calculate the trigonometric ratios.

Not just any triangle will do for trigonometry, though.

It has to be a right triangle where one of the angles is a 90 degree angle.

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