Math141HW4

Math141HW4 - (Exercises for Chapter 5 Analytic Trigonometry...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

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

Unformatted text preview: (Exercises for Chapter 5: Analytic Trigonometry) E.5.1 CHAPTER 5: Analytic Trigonometry (A) means “refer to Part A,” (B) means “refer to Part B,” etc. (Calculator) means “use a calculator.” Otherwise, do not use a calculator. Write units in your final answers where appropriate. Try to avoid rounding intermediate results; if you do round off, do it to at least five significant digits. (Exercises for Chapter 5: Analytic Trigonometry) E.5.2 SECTION 5.1: FUNDAMENTAL TRIGONOMETRIC IDENTITIES Ignore domain issues in these problems. 1) Complete the Identities. Fill out the table below so that, for each row, the left side is equivalent to the right side, based on the type of ID given in the last column. (A) Left Side Right Side Type of ID csc x Reciprocal ID tan x Reciprocal ID tan x Quotient ID tan ¡ 2 ¢ x £ ¤ ¥ ¦ § ¨ Cofunction ID cos x Cofunction ID sin ¡ x ( ) Even / Odd (Negative-Angle) ID cos ¡ x ( ) Even / Odd (Negative-Angle) ID tan ¡ x ( ) Even / Odd (Negative-Angle) ID sin 2 x + cos 2 x Pythagorean ID tan 2 x + 1 Pythagorean ID 1 + cot 2 x Pythagorean ID (Exercises for Chapter 5: Analytic Trigonometry) E.5.3 2) Simplify the following. Find the most “compact” equivalent expression. (A-F) a) 1 ¡ sec ¡ x ( ) 1 ¡ cos ¡ x ( ) b) tan ¡ + cot ¡ cot ¡ c) sec 2 x ¡ sec 2 x sin 2 x d) cot 4 x + 2cot 2 x + 1 e) sin ¡ 2 ¢ t £ ¤ ¥ ¦ § ¨ cot t f) csc ¡ + cot ¢ ¡ ( ) £ ¤ ¥ ¦ 1 + cos ¢ ¡ ( ) £ ¤ ¥ ¦ 3) Use the given trigonometric substitution to rewrite the given algebraic expression as a trigonometric expression in ¡ , where ¡ is acute. Simplify. (These types of substitutions are used in an advanced integration technique in calculus.) (G) a) Substitute x = 4 sin ¡ in the expression 16 ¡ x 2 . b) Substitute x = 6 tan ¡ in the expression x 2 + 36 . c) Substitute x = 3sec ¡ in the expression x 2 ¡ 9 . (Exercises for Chapter 5: Analytic Trigonometry) E.5.4 SECTION 5.2: VERIFYING TRIGONOMETRIC IDENTITIES Ignore domain issues in these problems. 1) Verifying the following identities. (A-C) a) 1 ¡ sin ¡ x ( ) cos ¡ x ( ) = sec x + tan x b) sin u cos u ¡ cos u sin u ¡ sin 2 u = ¡ cot u c) 1 tan ¡ ¢ tan ¢ ¡ ( ) = csc ¡ sec ¡ d) 1 csc x + 1 + 1 csc x ¡ 1 = 2sec x tan x e) 1 ¡ cos ¢ 1 + cos ¢ = 1 ¡ cos ¢ sin ¢ f) 1 1 ¡ cos ¢ = csc 2 ¢ + csc ¢ cot ¢ g) tan 5/2 x + tan 1/2 x = sec 2 x ( ) tan x (Exercises for Chapter 5: Analytic Trigonometry) E.5.5 SECTION 5.3: SOLVING TRIGONOMETRIC EQUATIONS Use radian measure for angles in the following problems. Give exact solutions. 1) For each of the equations below, find all real solutions, and find the particular solutions in the interval 0, 2 ¡ [ ) ....
View Full Document

This note was uploaded on 02/07/2012 for the course MATH 2203 taught by Professor Ellermeyer during the Fall '10 term at FIU.

Page1 / 16

Math141HW4 - (Exercises for Chapter 5 Analytic Trigonometry...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online