http://www.ck12.org Chapter 8. Right Triangle Trigonometry
8.6 Sine, Cosine, Tangent
Here you’ll learn what the three trigonometric ratios are and how to find their value for a right triangle’s non-right
angle.
What if you were given a right triangle and told that its sides measure 3, 4, and 5 inches? How could you find the
sine, cosine, and tangent of one of the triangle’s non-right angles? After completing this Concept, you’ll be able to
solve for these trigonometric ratios.
Watch This
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Click image to the left for more content.CK-12 Foundation: Chapter8SoneCosineTangentA
Watch the parts of the video dealing with the sine, cosine, and tangent.
MEDIA
Click image to the left for more content.James Sousa:Introduction toTrigonometric FunctionsUsing Triangles
Guidance
The word trigonometry comes from two words meaning trianglemeasure. In this lesson we will define three
trigonometric (or trig) functions.
Trigonometry:The study of the relationships between the sides and angles of right triangles.
In trigonometry, sides are named in reference to a particular angle. The hypotenuse of a triangle is always the same,
but the termsadjacentandoppositedepend on which angle you are referencing. A side adjacent to an angle is the
leg of the triangle that helps form the angle. A side opposite to an angle is the leg of the triangle that does not help
form the angle. We never reference the right angle when referring to trig ratios.
The three basic trig ratios are called, sine, cosine and tangent. At this point, we will only take the sine, cosine and
tangent of acute angles. However, you will learn that you can use these ratios with obtuse angles as well.
Sine Ratio:For an acute anglexin a right triangle, the sinxis equal to the ratio of the side opposite the angle over
the hypotenuse of the triangle. Using the triangle above, sinA=acand sinB=bc.
Cosine Ratio:For an acute anglexin a right triangle, the cosxis equal to the ratio of the side adjacent to the angle
over the hypotenuse of the triangle.Using the triangle above, cosA=bcand cosB=ac.