Math141HW4

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

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

Page1 / 16

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

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