Contents of this Precalculus episode:

Trigonometric functions, Sine, Cosine, Period, Equation with sine, Equation with cosine, Tangent, Trigonometric identities, Trigonometric relationships.

Text of slideshow

And now it is time to name these coordinates.

The name of the x coordinate is... let’s say... Bob,

and the y coordinate...

Hmm... Maybe Bob isn’t such a good name after all... A name starting with C would sound better.

And the other one “sine”.

Will be right back...

The x coordinate of point P is called .

And the y coordinate is called .

A very typical case is when a quadratic equation disguises itself as a trigonometric equation.

Here is one like that:

Here comes the solution formula:

Cosine is always between -1 and 1,

thus, the first case is not very likely.

Let’ see what happens in the other case.

Another typical trick is when we first use this identity in the equation, and that’s how we get a quadratic equation.

Let's see one like this, too.

The first degree term in the equation is cosx,

so it would be best if we had cosx everywhere.

And now let’s see a more exciting equation.

The sine function works so that the blue solution is given by the calculator,

and the green solution can be found based on the fact that the sum of the two angles always has to be a straight angle.

Cosine is much more pleasant, here the blue solution is given by the calculator,

and the green one is the negative of it.

Tangent works so that the blue solution is given by the calculator,

and the period is not , but .

Cosine works the usual way.

# Trigonometric equations

03
Let's see this
Precalculus episode