Trigonometric Identities - Miami
1+cos 2 tan 2 = q 1+cos tan 2 = 1 cosx sinx tan 2 = sin 1+cos Double-Angle Formulas sin2 = 2sin cos cos2 = cos2 sin2 tan2 = 2tan 1 tan2 cos2 = 2cos2 1 cos2 = 1 2sin2 Product-to-Sum Formulas sinxsiny= 1 2 [cos(x y) cos(x+ y)] cosxcosy= 2 [cos(x y) + cos(x+ y)] sinxcosy= 1 2 [sin(x+ y) + sin(x y)] Sum-to-Product Formulas sinx+ siny= 2sin x+y 2
TRIGONOMETRY LAWS AND IDENTITIES
TRIGONOMETRY LAWS AND IDENTITIES QUOTIENT IDENTITIES tan(x)= sin(x) cos(x) cot(x)= cos(x) sin(x) RECIPROCAL IDENTITIES csc(x)= 1 sin(x) sec(x)= 1 cos(x) cot(x)= 1 tan(x) sin(x)= 1 csc(x)
SOME BASIC TRIGONOMETRY - KNOW THIS FUNDAMENTAL
1 cos(x) cot(x)= 1 tan(x) sin(x)= 1 csc(x) cos(x)= 1 sec(x) tan(x)= 1 cot(x) Warning: The reciprocal of sin(x) is csc(x), not sec(x) Note: We typically treat “0” and “undefined” as reciprocals when we are dealing with basic trigonometric functions Your algebra teacher will not want to hear this, though Quotient Identities tan(x)= sin
Math 123 - College Trigonometry Euler’s Formula and
eix = cos(x) + isin(x) (1) Where e is the base of the natural logarithm (e = 2:71828:::), and i is the imaginary unit Using this formula you can derive most of the trigonometric identities/formulas (sum and
Domain, Range, and Period of the three main trigonometric
cos 1(cos 4ˇ 5 ) = 4ˇ 5, since 0 4ˇ 5 ˇ Bad II: is in the right quadrant, but written incorrectly cos 1(cos 6ˇ 5 ) = ? Now 6ˇ 5 is not between 0 and ˇ, but it is in the right quadrant, namely quadrant II To nd the correct angle, simply add or subtract 2ˇfrom the angle given until you get an angle in the range of cos 1(x) In this case
Complex numbers and Trigonometric Identities
(cos (x –y), sin (x – y)) (1, 0) Figure 1 Figure 2 Find cos ????????−????????based on the unit circle Distance between the two labeled points in Figure 1
MATH 1A - HOW TO SIMPLIFY INVERSE TRIG FORMULAS
cos(sin 1(x)) 2 = 1 x2 + cos(sin 1(x)) 2 = 1 cos(sin 1(x)) 2 = 1 x2 cos(sin 1(x)) = p 1 x2 Now the question is: Which do we choose, p 1 x2, or p 1 x2, and this requires some thinking The thing is: We defined sin 1(x) to have range [ˇ 2; ˇ 2] so, cos(sin 1(x)) has range [0;1], and is in particular 0 (see picture below for more clarification
Trig Cheat Sheet - Lamar University
cos hypotenuse q= hypotenuse sec adjacent q= opposite tan adjacent q= adjacent cot opposite q= Unit circle definition For this definition q is any angle sin 1 y q==y 1 csc y q= cos 1 x q==x 1 sec x q= tan y x q= cot x y q= Facts and Properties Domain The domain is all the values of q that can be plugged into the function sinq, q can be any
Commonly Used Taylor Series
X1 n=0 xn n x 2R cosx = 1 x2 2 + x4 4 x6 6 + x8 8::: note y = cosx is an even function (i e , cos( x) = +cos( )) and the taylor seris of y = cosx has only even powers = X1 n=0 ( 1)n x2n (2n) x 2R sinx = x x3 3 + x5 5 x7 7 + x9 9::: note y = sinx is an odd function (i e , sin( x) = sin(x)) and the taylor seris of y = sinx has only odd
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