Our next batch of identities makes heavy use of the

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: √ √ 1 , − 23 2 (0, −1) Important Points on the Unit Circle 6 For once, we have something convenient about using radian measure in contrast to the abstract theoretical nonsense about using them as a ‘natural’ way to match oriented angles with real numbers! 620 Foundations of Trigonometry The next example summarizes all of the important ideas discussed thus far in the section. Example 10.2.4. Suppose α is an acute angle with cos(α) = 5 13 . 1. Find sin(α) and use this to plot α in standard position. 2. Find the sine and cosine of the following angles: (a) θ = π + α (b) θ = 2π − α (c) θ = 3π − α (d) θ = π 2 +α Solution. 5 1. Proceeding as in Example 10.2.2, we substitute cos(α) = 13 into cos2 (α) + sin2 (α) = 1 and 12 find sin(α) = ± 13 . Since α is an acute (and therefore Quadrant I) angle, sin(α) is positive. Hence, sin(α) = 12 . To plot α in standard position, we begin our rotation on the positive 13 5 x-axis to the ray which contains the point (cos(α), sin(α)) = 13 , 12 . 13 y 1 5 12 13 , 13 α 1 x Sketching α 2. (a) To find the cosine and sine of θ = π + α, we first plot θ in standard position. We can imagine the sum of the angles π + α as a sequence of two rotations: a rotation of π radians followed by a rotation of α radians.7 We see that α is the reference angle for θ, so by 5 12 The Reference Angle Theorem, cos(θ) = ± cos(α) = ± 13 and sin...
View Full Document

This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online