Defining Trigonometric Ratios Adapted from Walch Education
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Defining Trigonometric Ratios The three main ratios in a right
triangle are the sine, the cosine, and the tangent. These ratios
are based on the side lengths relative to one of the acute
angles.
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Now that seemed Important and Super Duper Interesting!!!!
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The acute angle that is being used for the ratio is known as
the reference angle. It is commonly marked with the symbol (theta)
but can also be written using the Greek letter phi. ( )
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WHAT !?!?!? SOMEONE WILL NEED TO EXPLAIN THAT LAST SLIDE TO
ME.
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HMMM just a wild guess>>>> the reciprocal of sine
is cosecant; the reciprocal of cosine is secant; and the reciprocal
of tangent is cotangent. BUT WHATS A RECIPROCAL ? SOMEONE DEFINE
THIS FOR ME.THANKS!
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Back to this again How do I know which leg is considered the
adjacent side and which is the opposite side? FOOD FOR THOUGHT
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ARE WE READY FOR AN EXAMPLE? I think so Find the sine, cosine,
and tangent ratios for and in the triangle. Convert the ratios to
decimal equivalents.
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Somethings Missing, yikes! So, a = 4 and b = 3, so what is the
length of the hypotenuse, c? Thank you Pythagorean Theorem for
saving the dayonce again. Since c is a length, use the positive
value, c = 5.
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GREAT! Now what? HINT>>> Set up the ratios using the
lengths of the sides and hypotenuse, and while youre at itconvert
to decimal form.
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OKAY, Finding the sine, cosine, and tangent of is all up to
you!