LEARNING TARGETS AFTER YOU COMPLETE THIS CHAPTER, YOU WILL BE ABLE TO: DEFINE TRIGONOMETRIC RATIOS CHANGE MEDIAN MEASURE TO DEGREE MEASURE DEFINE AND NAME TRIGONOMETRIC RATIOS IN SPECIAL TRIANGLES IDENTIFY GRAPHS OF SINE, COSINE, & TANGENT USE THE LAW OF SINES AND COSINES
TRIGONOMETRY RATIOS Trigonometry: Comes from the Greek word, “trigonon” or triangle and “metron” to measure. The main part of trigonometry is the right triangle. There are several special names that define the ratios. Cosine, Sine, and Tangent. They also have reciprocals (or the opposite)
Here is a chart of the ratios…..
Here is a list of reciprocal ratios…
Chapter Vocabulary Degree: 1/360 of a full circle – symbol = ⁰ Minute: 1/60 of a degree, so 1⁰ = 60’ Second: 1/60 of a minute, so 1’ = 60” Quadrant – four parts of a circle, using Roman Numerals and numbers counter-clockwise. Quadrant I = 0⁰ to 90⁰ Quadrant II = 90⁰ to 180⁰ Quadrant III = 180⁰ to 270⁰ Quadrant IV = 270⁰ to 360⁰
What does this look like? Radians – the angle between two radii of a circle, which is cut off on the circumference by an arc equal in length to the radius.
A 360⁰ Circle
Special Triangles 30 – 60 – 90 Triangle 45 – 45 – 90 Triangle There is a unique relationship to the sides in these triangles:
Basic Identities Reciprocal – opposites Pythagorean – using Pythagorean Theorem Quotient – using division Cofunction – one ratio working with another
The Unit Circle In the unit circle – the radius is 1. The right triangle for each quadrant is determined by the reference angle, the angle with the initial side at 0⁰.
Inverse Trigonometric Functions A quick look at the graph for cosine, sine, and tangent shows that there is one x and y value. They can pass the vertical line test. The inverse or opposite function cannot. Principal value: The value of a function in a restricted range. Arcsin, Arccos, Arctan are the inverse functions.
COFUNTCIONS AND COMPLEMENTARY ANGLES COFUNCTIONS OF COMPLETMENTARY ANGLES ARE EQUAL. COFUNTCION PAIRS:
SOLVING THE TRIANGLE Solving the triangle: the process to find the missing sides and angles. Law of Sines: