CLO 3: Simplify trigonometric functions and equations

Topic 3: TRIGONOMETRY

OVERVIEW

Trigonometry (Greek word trigonon triangle and metron measure) is the branch of mathematics that deals with the measurement of sides and angles of a triangle. Trigonometry has many applications in engineering, surveying, construction, and navigation. This module will be discussing the topics about radians and degrees, trigonometric functions, inverse trigonometric functions, and the graph of sine and cosine functions.

LEARNING OBJECTIVES

At the end of this module, you should be able to:

1. Convert between degrees and radians.

2. Solve trigonometric functions of any angle and solve real-life problems.

3. Determine the amplitude, period, and cycle of a sine and cosine graphs.

4. Sketch the graphs of sine and cosine.

Subtopic: STANDARD POSITION

An angle is in standard position when the vertex is at the origin, and the initial side is along the positive x-axis.

From the figure above, the green line has an angle of 30 degrees when measured counterclockwise and -330 degrees when clockwise. Same with the orange line, when measured clockwise, it is -105 degrees and 255 degrees when measured counterclockwise. These are examples of coterminal angles. Two angles which, when placed in standard position, have coincident terminal sides are called coterminal angles. (Moyer)

EXAMPLE:

Find two positive angles and two negative angles that are coterminal with 50°.

SOLUTION:

To solve the two positive angles that are coterminal with the given angle, we will add 360° and then add 360° again.

Positive Coterminal Angle 1 = 50° + 360° = 410°

Positive Coterminal Angle 2 = 50° + 360° + 360° = 770°

For the two negative angles that are coterminal with the given angle, we will subtract 360° , then subtract 360° again.

Negative Coterminal Angle 1 = 50° − 360° = −310°

Negative Coterminal Angle 2 = 50° − 360° − 360° = −670°

REFERENCES

Larson, R. (2016) Algebra and Trigonometry: Real Mathematics, Real People, 7th Edition. USA: Cengage Learning

Stewart, J., Redlin, L. and Watson, S. (2016) Algebra and Trigonometry, 4th Edition. USA: Cengage Learning

Sullivan, M. (2012) Trigonometry A Unit Circle Approach, 9th Edition. USA: Pearson Education, Inc.

Moyer, R. and Ayres, F. (2009) Schaum’s Outlines: Trigonometry, 4th Edition. USA: McGraw Hill

Aufmann, R., Baker, V. and Nation, R. (2011) College Algebra and Trigonometry, 7th Edition. USA: Broke/Cole, Cengage Learning

Rider, P. (1971) Plane and Spherical Trigonometry. New York: The Maximillian Company

https://www.khanacademy.org/humanities/big-history-project/solar-system-and-earth/knowing-solar-system-earth/a/eratosthenes-of-cyrene

https://www.youtube.com/watch?v=EfZ2HZH5CkA

PROBLEM SET 3

Reflection on Learning

Trigonometry was also one of the topics that was thought during our high school days and part of it is knowing the basics of sine, cosine, and tangent. For the third topic, I chose this problem because I know the solution but careless about the formula that I'm using. To answer this problem, knowledge regarding the formula for trigonometry is beneficial to use in real-life problems like this. To be specific, in answering the problem, it is a must to review the formula being used like in the equation, instead of using sine, the correct one must be tangent because the given are the angle (theta) and the adjacent measure. What is required to solve was the opposite measure which is why it corresponds to that kind of formula.

What I learned here is to be more careful of what to use because there is a saying that efforts are not paid off if you don't use the right tools. Relating here on this topic, it is better to use the time to be critical on what to use in solving real-life problems..