No matter how big or small a circle, or the units used to measure the circle's circumference and diameter, the ratio of the circle's circumference to its diameter is always the same number. The symbol π is the tag/label we use to identify the ratio of the circumference of a circle to its diameter.

_{}

The tags "sin", "cos", and "tan" are also symbols (albeit three letter symbols) used identify ratio of the sides of a triangle.

**Meaning of "sin", "cos", "tan"**__
__The ratio of two sides of any right triangle

There are three ways to form a ratio of the three sides of a triangle (six if you count the inverse ratios also). **The symbols "sin", "cos", and "tan" are the tags/labels we use to identify which ratio is which**.

.

**A right triangle is any triangle in which one of its angles is 90**^{o}.- In any right triangle there are
__two angles__that one could focus attention on besides the right angle. - The sum of these two angles is always equal to 90
^{o},**θ + φ**= 90^{o}. If you know one of the angles you can always find the other since it is the complement of the known angle, i.e. the other angle is equal to 90^{o}minus the known angle. - The side of the triangle that is the called the Hypotennuse is always the side opposite the right angle.
- When determining the sine, cosine, or the tangent of an angle, the Opposite and Adjacent sides for this angle is not the same as the other complementary angle. In fact they are the opposite of each other.

**Hypotenuse****: hyp**

The side opposite the right angle
**Opposite Side****: opp**

The side opposite the angle of focus.
**Adjacent Side****: adj**

The side connected to the angle of focus.

**Trigonometric Relations for either Angle:**

- If one chooses an angle first and labels the sides relative to that angle, then

_{}

- The advantage of this method is that it works regardless of the orientation of the triangle or the labels used for the angles - there is nothing sacrosanct about the labels
**q**and**f**.

- Note there is more than one angle that will give the same value of the trigonometric function or its inverse.

_{
}

Show Topics Menu Frames |