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Trigonometry: Law of Sines, Law of Cosines, and Area of Triangles. Formulas, notes, examples, and practice test (with solutions) Topics include finding angles and sides, the “ambiguous case” of law of Sines, vectors, navigation, and more.
Drawing the graphs of the trigonometric ratios can help us to see the change in signs as angles increase. We divide the domain 0 0 to 360 into 4 quadrants: geogebra activity angles of any magnitude NOTE: angles can be expressed as either DEGREES (what you are used to) or in RADIANS. Basically π = 180 0, so π = 90 0, = 45 etc. 2 4 π = 1 radian
DEPARTMENT OF MATHEMATICS AND STATISTICS MAST10012 Introduction to Mathematics Semester 1, 2011 REVISION - TRIGONOMETRY A: Finding trig ratios in the Unit Circle 1. Identify the quadrant that the angle is in: Q1 has angles from 0! ˇ 2 Q2 has angles from ˇ 2! ˇ Q3 has angles from ˇ! 3 ˇ 2 Q4 has angles from 3 ˇ 2! 2 ˇ Q 1 Q 2 Q 3 3 Q 4
Some special angles and their trigonometric ratios. In the examples which follow a number of angles and their trigonometric ratios are used frequently. We list these angles and their sines, cosines and tangents.
Double Angle and Half Angle Formulas 26. sin(2 ) = 2 sin cos 27. cos(2 ) = cos2 sin2 28. tan(2 ) = 2 tan 1 2tan 29. sin 2 = r 1 cos 2 30. cos 2 = r 1+cos 2 31. tan 2 = 1 cos sin = sin 1 cos 32. tan 2 = r 1+cos 1 cos Other Useful Trig Formulas Law of sines 33. sin = sin = sin Law of cosines 34. a2 = b2 +c2 2 b c cos b2 = a2 +c2 2 a c cos c2 = a2 ...
Graphs of the Trigonometric Functions Find each value by referring to the graphs of the trigonometric functions. 1. sin (-720 °) 2. tan (-180 °) 3. cos (540 °)
Section 1. Review of Trig Ratios. Worksheet 2:8 introduces the trig ratios of sine, cosine, and tangent. To review the ratios, consider a triangle ABC with angle as marked. . B. A b C The hypotenuse (hyp) of the triangle is c; the adjacent (adj) side is b; the opposite (opp) side is a.
