To nd where this equivalence is valid we x tan2 rst

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 − 2 sin2 (θ) • sin(2θ) = 2 sin(θ) cos(θ) • tan(2θ) = 2 tan(θ) 1 − tan2 (θ) The three different forms for cos(2θ) can be explained by our ability to ‘exchange’ squares of cosine and sine via the Pythagorean Identity cos2 (θ) + sin2 (θ) = 1 and we leave the details to the reader. It is interesting to note that to determine the value of cos(2θ), only one piece of information is required: either cos(θ) or sin(θ). To determine sin(2θ), however, it appears that we must know both sin(θ) and cos(θ). In the next example, we show how we can find sin(2θ) knowing just one piece of information, namely tan(θ). Example 10.4.3. 1. Suppose P (−3, 4) lies on the terminal side of θ when θ is plotted in standard position. Find cos(2θ) and sin(2θ) and determine the quadrant in which the terminal side of the angle 2θ lies when it is plotted in standard position. 2. If sin(θ) = x for − π ≤ θ ≤ π , find an expression for sin(2θ) in terms of x. 2 2 3. Verify the identity: sin(2θ) = 2 tan(θ) . 1 + tan2 (θ) 4. Express cos(...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online