Unpacking Trig Ratios: Understanding Sine, Cosine, Tan, and More

AI Thread Summary
Understanding trigonometric ratios in terms of sine, cosine, tangent, cosecant, secant, and cotangent is crucial for simplifying equations and functions in various mathematical contexts. These ratios are foundational for expressing values in two dimensions, particularly in circular functions. The reciprocal and ratio forms facilitate easier calculations and interpretations in trigonometry. Additionally, the use of tangent helps quantify angles between vectors that may be oriented differently. Mastery of these concepts is essential for solving complex problems in geometry and physics.
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Homework Statement



What is the importance of knowing how to express trig ratios in terms of sine, cosine, tan, cosec, sec, or cot?



Homework Equations





The Attempt at a Solution

 
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What is the attempt at the solution? Did you think this through?
 
I already know how to do it... I just want to know what the importance is...
for example...
Sin with respect to tan is sin/(1-sin^2)^(1/2)
W/ respect to sec... 1/(i-sin^2)^(1/2)...
and so on..
 
The main cofunctions are for expressing values in two dimensions, since Trigonometric functions are circular functions. The reciprocal and ratio forms of these functions allow for some simpler terms when writing equations or functions for specific topics which use Trigonometry. Note also that vectors may be in different directions and by that be at an angle to each other; this justifies the use of Tangent to help in quantifying or describing the angle (remember when you learned that in a plane the the product of the slopes of perpendicular lines is negative one?).
 

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