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Featured 7 months ago

See below:

With a triangle with

We could run through the pythagorean theorem for the third side, but we can also remember that these two measurements are part of a 30-60-90 triangle, and so the third side is

This gives us the 6 trig ratios:

The angle of the triangle we're looking at is

Featured 6 months ago

The angle

When we talk about the quadrant an angle is in, we're really talking about the quadrant the *terminal arm* of the angle is in, when the angle is drawn with its initial arm along the

To draw an angle, imagine a clock centered at the origin, with the minute hand pointing to the right (at the "3"). Then, rotate the hand counterclockwise (towards the "12") by the amount of the angle. Since the angle

Now,

Which quadrant is this? The quadrants are named in increasing order, starting with quadrant 1 (

So the angle

Featured 3 months ago

Use the double angle formula for cosine to expand

Let

Featured 2 months ago

The given function representing the height

(a) h is a cosine function of t, So it will have maximum value when

and the maximum height of the swing becomes

(b) it takes

c) The minimum height of the swing will be achieved when

Minimum height

(d). Again

Here

e) For

when

So in

f) The height of the swing at 10 s can be had by inserting

Featured 2 months ago

Strategy: Rewrite this equation as a quadratic equation using

Step 1. Rewrite this equation as a quadratic using

You are given

Replace

Step 2. Factor the quadratic equation.

Solving gives us

Step 3. Replace

These answer work because we were asked to find the solutions in

However, the graph of

Which shows **four** solutions in the interval

We must find the other solutions by recognizing that sine functions are periodic with respect to

So,

The other two solutions are

Featured 2 months ago

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