**Trigonometry Online Tutoring Review **

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Online Review of Trigonomerty Lesson One

This lesson shows the deriviation of the cosine, sine and ttangent for the 30, 45 and 60 degree angles. The 45 degree values are obtained from the geometry of a square and the 30 and 60 degree values are determined from the geometry of an equalateral triangle.

Once you know how to determine the sine, cosine and tangent values for 30, 45 and 60 degrees, you can use the double angle trigonometric identities to find the cosine, sine and tangent values for a multitiude of angles. All without the use of a calculator!!

Review of geometry

Areas of Basic Geometric Shapes

Pythagorean Theorem

Basic Trigonometric Idenites

Figure 1: Basic Geometric and Trigonometric Formulas

Congruent and Similar Triangles

Equalateral Triangle: Prove that the two triangles (ABC and CDB) contruscted within am equalateral triangle are congruent. The line CD bisects line AB.

When a transversal intersects two parallel lines, all angles formed that are greater than 90 degrees have the same measure and all angles formed that less than 90 degrees have the same measure (congruent).

Complimentary angles in a triangle add to 90 degrees.

Proving a triangle within a triangle are similar to each other requires that you use the fact that corresponding angles of two parallel lines cut by a transversal are equal (the smaller angles).

Proving similar triangles

Establishing proportional relationships between lines in similar triangles.

Distance Formula Example Problem

Calculate the distance between two points (between point (1,4) and (4,1)

Calculate the midpoint of a line given two points with the midpoint formula

Given two angles in a triangle find the measure of the third angle. If one angle is 30 and the other is 90, what is the value of angle A.

Find the area of a triangle given a perpendicular bisector, and the length of two sides of the triangle

Given AB = 10, CD is a perpendicular bisector of AB and CB = 8 find the area of the triangle, ABC

The answer is 5*Math.Sqrt(39)

Find the sine, cosine and tangent of a 3,4, 5 triangle

The length of an arc on a circle.

Find the area, circumference and diameter of a circle given the radius.

Definition of a radian in terms of degrees in a circle.

Radians to Degrees Conversion Factor and sample problem

Convert 36 degrees to radians

Convert radians to degrees

TI-84 Calculator Notes for changing from degree mode to radian mode.

List of commonly used angles in trig expresssed in degrees and radians.

Given the measure of an arc on a circle is equalt to 0.3 inches, and the radius is 3 inches, find the measure of the arc angle.

The answer is 5.76 degrees.

Converting degrees to radians

Convert 5.76 degrees to radians

Degrees per Radian conversion

Plotting a sine wave: Amplitude versus time

Plot a cosine wave: Amplitude versus time

Plot of sine waves

At a frequency of 1 Hz (1 Cycle per Second)

At a frequency of 2 Hz (2 Cycles per Second)

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