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Trigonometry Online Tutoring Review

For questions email: mark.c.stansberry@gmail.com.

To schedule or resechedule a tutoring appointment email or call/text (707)235-4095.

 

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

 

 

 

 

 

 

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Congruent and Similar Triangles

 

 

 

 

 

 

 

 

 

 

 

 

 

trionometry tutoring lesson side angle side congruent triangles

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

 

 

 

 

 

 

 

 

 

 

 

 

 

santa rosa trigonometry tutoring lesson geometry review congruent angles transversal parallel lines supplementary anglesWhen 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).

 

 

 

 

 

 

 

 

 

 

 

 

 

santa rosa trionometry tutoring lesson complimentary angles supplementary angles similar triangles

 

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).

 

 

 

 

 

 

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Proving similar triangles

 

 

 

 

 

 

 

Establishing proportional relationships between lines in similar triangles.

 

 

 

 

 

santa rosa trigonometry tutoring lesson geometry review distance and midpoint formulasDistance 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.

 

 

santa rosa online trigonometry tutoring problems and solutions for trig problems 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)

 

 

 

 

 

 

santa rosa tutoring online trigonometry lessons trigonometric proofs tan equalt to sine divided by cosine

 

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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

santa rosa online tutoring trigonometry circles radians lessons circumference arc measure

 

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.

 

 

 

santa rosa online tutoring trigonometry lessons radian to degrees conversion factor ZIP 95405

Radians to Degrees Conversion Factor and sample problem

 

 

Convert 36 degrees to radians

 

 

 

 

 

Convert radians to degrees

 

 

 

 

 

santa rosa online tutoring trigonometry TI 74 degree mode and radian mode instructions buttons steps

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

 

 

 

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

 

 

 

 

 

 

 

 

 

santa rosa online tutoring trigonometry lesson problem solution given arc length find the measure of the angleGiven 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.

 

 

 

 

santa rosa online tutoring trigonometry lesson sine wave plotting as a function of time

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

 

 

 

 

 

 

 

 

 

 

 

santa rosa online tutoring trigonometry lessons sinewave plotting at different frequencies

Plot of sine waves

 

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

 

 

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

 

 

 

 

 

 

 

 

 

 

 

 

 

santa rosa tutoring trigonometry lesson sine cosine tangent trigonometric identities sample problems

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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