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8-3 8-4 Sine, Cosine and Tangent Ratios
ObjectiveStudents will be able to use sine, cosine, and tangent ratios to determine side lengths in triangles.
Trigonometric Ratios• We use the Pythagorean Theorem when we are given two
sides of a right triangle and we want to find the third.• We will use trigonometric ratios when we are given one side
and one angle (other than the 90 degree angle) of a right triangle and want to find another (or both) side(s).
• There are three trigonometric ratios we will utilize• Sine (abbreviated sin)• Cosine (abbreviated cos)• Tangent (abbreviated tan)
Side Definitions
• Opposite side: leg directly across from the angle of interest• Adjacent side: leg next to the angle of interest• Hypotenuse: side directly across from the right angle• The opposite and adjacent sides differ depending on the
angle of interest. For example, if you are looking at angle X, then the opposite side is a. However, if you are looking at angle Y, then the opposite side is b.
Other notes• Never use the right angle when using trigonometric ratios.
Only use one of the two acute angles.• Calculators must be in “degree” mode. To check, press the
“mode” button and go down to where you see “radian” and “degree”. If not already highlighted, highlight “degree” and press enter.
• If your calculator is in “radian” mode, you will not get the correct answers we are looking for here. (They are correct answers but for Geometry we want answers in Degree Mode)
Finding Side Length• When using trigonometry
to solve for a side length, first determine which trig ratio to use based on the given information.• Then, substitute in the
information.• Finally, solve as you would
solve a proportion. We usually round to the nearest tenth.
Finding Angle Measures
• If given two sides of a right triangle, we can determine the angle measures by using inverse trigonometric ratios.• Start by determining the appropriate ratio to use
and substituting in your information. • Then, take the inverse of the ratio.• To do this on the calculator, hit “2nd” and then
hit either sin, cos, or tan (depending on which ratio is appropriate given the problem).