SOHCAHTOA

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apple2357

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I was talking to someone the other day who was telling me they never learnt SOHCAHTOA to solve right angled triangles problems at school. Instead they were introduced to the unit circle and were told the x coordinate was cos( theta) and the y coord was sin(theta).

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And then every trig problem can be done through scaling ( i think?).

Is this approach familiar to anyone and what do they see as the benefits of this over SOHCAHTOA?

I guess i am saying what is the definition of these functions? Clearly there is consistency between the two ways of thinking. But i am curious why one approach might be used instead of the other.

I understand these ideas are typically taught at the age of 13.
 
The beauty about the unit circle approach is that it applies to all angles, not just acute angles, which appear in a right-angled triangle.

SOHCAHTOA can only be used in right-angled triangles (because only a right angled triangle has a hypotenuse).

The more concrete examples, at an introductory level, involve right angled triangles and acute angles. I have always taught SOHCAHTOA first. And then brought in the concept of the unit circle prior to considering non-acute angles.
 
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Harry_the_cat said:
The beauty about the unit circle approach is that it applies to all angles, not just acute angles, which appear in a right-angled triangle.

SOHCAHTOA can only be used in right-angled triangles (because only a right angled triangle has a hypotenuse).

The more concrete examples, at an introductory level, involve right angled triangles and acute angles. I have always taught SOHCAHTOA first. And then brought in the concept of the unit circle prior to considering non-acute angles.
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But how does the unit circle approach help you solve non right-angled triangle problems? The coordinates of the point don't necessarily tell you the lengths of the non right angled triangle?
 
No, but it enables you to calculate sin(120 degrees) for example.
I'm not sure what your background is or what level you are at, but do you know about the Law of Sines (sometimes called the Sine Rule) or the Law of Cosines (Cos rule)?
 
I am very experienced in trigonometry and never once used unit circles except maybe to prove a few theorems. I go purely by the definitions of the six trig functions and never had any trouble solving problems.

I think (ie I am probably wrong) that one learns trig from the definitions or the unit circle.
 
Jomo said:
I go by the definition of the six trig functions. The usual ones, SOHCAHTOA.
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But that applies only to acute angles. Do you mean, perhaps, the extension of the right-triangle definitions to the entire plane? E.g. sin(theta) = y/r, for a point (x,y) on the line at angle theta and distance r from the origin? That's my preferred definition.
 
Trigonometry, as its name implies, started as a tool for measuring triangles. That is still a practical need in surveying, navigation, architecture, etc.

It makes sense to introduce it that way.

The definitions deal with right triangles, but every triangle can be decomposed into two right triangles.

The concept of angles applies to other closed geometric figures such as the circle. And corresponding to a segment of a semi-circle is an isosceles triangle with the circle’s radius being the two equal legs and the chord of the arc being the base of trangle. Because the trigonometric functions are ratios, we might as say the radius is one unit and simplify the arithmetic. Hence “unit circle.”
 
Dr.Peterson said:
But that applies only to acute angles. Do you mean, perhaps, the extension of the right-triangle definitions to the entire plane? E.g. sin(theta) = y/r, for a point (x,y) on the line at angle theta and distance r from the origin? That's my preferred definition.
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I use reference angles for angles larger than 90. I use (ie think about) the graphs for 90, 180, 270.
 
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