Tanx cotx 2 sec 2x csc 2x
What is the trig identity of Tanx?
USEFUL TRIGONOMETRIC IDENTITIES De\fnitions tanx= sinx cosx secx= 1 cosx cosecx= 1 sinx cotx= 1 tanx Fundamental trig identity (cosx)2+(sinx)2= 1 1+(tanx)2= (secx)2 (cotx)2+1 = (cosecx)2
What is the solution of Tanx 4?
A common result, which you should know (and learn if you don’t), is that tan π 4 = 1. So x = π 4 is one solution of tanx = 1. Inspection of the graph, and using its periodicity, yields the second solution, x = 5π 4 . We can also deduce solutions of tanx = −1 from the same graph. These are x = 3π 4 and 7π 4 .
Do sec x and tan x have the same domains?
Thus, sec x and tan x have the same domains. The range of sec x is a bit more complicated: remember that the bounds on cosx are ¡1 · cos x · 1. So, we see that if the secant of x is positive, then it can be no smaller than 1, and if it is negative, it can be no larger than ¡1.
How do you re-write a Tanx equation?
We can use the identity sec2x = 1+tan2x to re-write the equation solely in terms of tanx: 2tan2x = sec2x 2tan2x = 1+tan x from which tan2x = 1 Taking the square root then gives tanx = 1 or − 1 The graph of tanx between 0 and 2π is shown in Figure 2. Note that the function values repeat every π radians. –1 1 2 4 3 4 5 4 7 4x tan x
[PDF File]Basic trigonometric identities Common angles
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2 x) = cosx cos(ˇ 2 x) = sinx tan(ˇ 2 x) = cotx cot(ˇ 2 x) = tanx sec(ˇ 2 x) = cscx csc(ˇ 2 x) = secx Sum and di erence of angles sin(x+y) = sinxcosy+cosxsiny sin(x y) = sinxcosy cosxsiny cos(x+y) = cosxcosy sinxsiny cos(x y) = cosxcosy+sinxsiny tan(x+y) = tanx+tany 1 tanxtany tan(x y) = tanx tany 1+tanxtany Double angles sin(2x ...
[PDF File]USEFUL TRIGONOMETRIC IDENTITIES - The University of Adelaide
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cotx= 1 tanx Fundamental trig identity (cosx)2 +(sinx)2 = 1 1+(tanx)2 = (secx)2 (cotx)2 +1 = (cosecx)2 Odd and even properties cos( x) = cos(x) sin( x) = sin(x) tan( x) = tan(x) Double angle formulas sin(2x) = 2sinxcosx cos(2x) = (cosx)2 (sinx)2 cos(2x) = 2(cosx)2 1 cos(2x) = 1 2(sinx)2 Half angle formulas sin(1 2 x) 2 = 1 2 (1 cosx) cos(1 2 x ...
[PDF File]Chapter 3.7: Derivatives of the Trigonometric Functions
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(cotx) = csc2 x. d dx (cotx) = d dx cosx sinx = (sinx)( sinx) (cosx)(cosx) sin2 x = 2(sin x+ cos2 x) sin2 x = 1 sin2 x = csc2 x 4. Use the quotient rule to show that d dx (cscx) = cscxcotx. d dx (cscx) = d dx 1 sinx = (sinx)(0) (1)(cosx) sin2 x = cosx sin2 x = 1 sinx cosx sinx = cscxcotx 2
[PDF File]TRIGONOMETRY LAWS AND IDENTITIES - CSUSM
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PYTHAGOREAN IDENTITIES. cos2(x) + sin2(x) = 1 tan2(x) + 1 = sec2 (x) cot2(x) + 1 = csc2 (x) SUM IDENTITIES. sin(x + y) = s in(x) cos(y) + cos(x) sin(y) cos(x + y) = cos(x) cos(y) - sin(x) sin(y) tan(x) + tan(y) tan(x + y) =. - tan(x) tan(y) DIFFERENCE IDENTITIES.
[PDF File]Trigonometric Identities
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derive three important identities use these identities in the solution of trigonometric equations Contents Introduction 2 Some important identities derived from a right-angled triangle sin2 A + cos2 A = 1 sec2 A = 1 + tan2 A Using the identities to solve equations cosec2A = 1 + cot2A 2 4
[PDF File]2.2 Graphs of tan(x), cot(x), csc(x) and sec(x) - NR
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64 2.2 Exercises Graphs and Inverse Functions For Exercises 1-9, determine the amplitude, period, vertical shift, horizontal shift, and draw the graph of the given function for two complete periods. y = 3 tan x 4. f(x) = 3 sec( x) 7. y = tan x + 4 2. f(x) = 3 csc x cot x 5. y = 4 8. y = 1 2 cot x 4 = y 3. 3 sec(2x) 6. y = cot 4
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