Defining Trigonometric Ratios Adapted from Walch Education

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.

Now that seemed Important and Super Duper Interesting!!!!

 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. (  )

WHAT !?!?!? SOMEONE WILL NEED TO EXPLAIN THAT LAST SLIDE TO ME.

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 WHAT’S A RECIPROCAL ? SOMEONE DEFINE THIS FOR ME….THANKS!

Back to this again… How do I know which leg is considered the adjacent side and which is the opposite side? FOOD FOR THOUGHT

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.

Something’s Missing, yikes!  So, a = 4 and b = 3, so what is the length of the hypotenuse, c?  Thank you Pythagorean Theorem for saving the day…once again.  Since c is a length, use the positive value, c = 5.

GREAT! Now what? HINT>>> Set up the ratios using the lengths of the sides and hypotenuse, and while you’re at it…convert to decimal form.

OKAY, Finding the sine, cosine, and tangent of is all up to you!

Thank You For Watching !!! ~ Ms. Dambreville