Stitz-Zeager_College_Algebra_e-book

Since is a quadrant ii angle 13 cos 12 we now set

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: θ) = 0 are quadrantal angles whose terminal sides, when plotted in standard position, lie along the y -axis. y y 1 1 π 2 x x 1 1 π 2 While, technically speaking, π isn’t a reference angle we can nonetheless use it to find our 2 answers. If we follow the procedure set forth in the previous examples, we find θ = π + 2πk 2 π and θ = 32 + 2πk for integers, k . While this solution is correct, it can be shortened to θ = π + πk for integers k . (Can you see why this works from the diagram?) 2 One of the key items to take from Example 10.2.5 is that, in general, solutions to trigonometric equations consist of infinitely many answers. To get a feel for these answers, the reader is encouraged to follow our mantra from Chapter 9 - that is, ‘When in doubt, write it out!’ This is especially important when checking answers to the exercises. For example, another Quadrant IV solution to sin(θ) = − 1 is θ = − π . Hence, the family of Quadrant IV answers to number 2 above could just 2 6 have easily been written θ = − π + 2πk for integers k . While on the surface, this family may look 6 10.2 The Unit Circle: Cosine and Sine different than the stated solution of θ = they represent the same list of angles. 10.2.1 11π 6 625 + 2πk for integers k , we leave it to the reader to show Beyond the Unit Circle We began the section with a quest to describe the position of a particle experiencing circular motion. In defining the cosine and sine func...
View Full Document

Ask a homework question - tutors are online