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Exporing the six basic trigonometry functions

Author:Shiva Latchmansingh
Topic:Functions

Find sin, cos, and tan

How do you find sin, cos, and tan? What does SOH CAH TOA stand for? What are the reciprocal of sin, cos, and tan?

Practice Skills

How do you find the six basic trigonometric functions. Which ones are important?

You are given a right triangle. Theta is located ACROSS from the right angle. The hypotenuse is 25, the flat side of the triangle is 8, and the opposite of theta is 13. What is csc, sec, and cot?

Explain what SOH CAH TOA is and how do you use it. What does the acronym stand for?

Help Center

There are six functions that are the core of trigonometry. There are three primary ones that you need to understand completely:
  • Sine  (sin)
  • Cosine  (cos)
  • Tangent  (tan)
The other three are not used as often and can be derived from the three primary functions. Because they can easily be derived, calculators and spreadsheets do not usually have them.
  • Secant  (sec)
  • Cosecant  (csc)
  • Cotangent  (cot)
All six functions have three-letter abbreviations (shown in parentheses above).Definitions of the six functionsConsider the right triangle on the left. For each angle P or Q, there are six functions, each function is the ratio of two sides of the triangle. The only difference between the six functions is which pair of sides we use.In the following table
  • a is the length of the side adjacent to the angle (x) in question.
  • o is the length of the side opposite the angle.
  • h is the length of the hypotenuse.
"x" represents the measure of ther angle in either degrees or radians. From Math Open Reference 

Critical Questions

Why do you think that csc, sec, and cot are easily less deprived? Why isn't it important? How and why is sin, cos, and tan important? Where and when in the world of trigonometry is it used? Give at least three examples. Do we need trigonometry? Why or why not?

Define what opposite, adjacent, and hypotenuse mean. When do we use them?

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