Math Notes - Math Notes 6.1 y = sin-1 x x = sin y y = cos-1...

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Unformatted text preview: Math Notes 6.1 y = sin-1 x x = sin y y = cos-1 x x = cos y y = tan-1 x x = tan y 6.2 y = sec-1 x x = sec y y = csc-1 x x = csc y y = cot-1 x x = cot y 6.3 Quotient Identities: tan = sin /cos cot = cos /sin Reciprocal Identities: csc = 1/sin sec = 1/cos cot = 1/tan 6.4 Sum & Difference Formulas: cos( + ) = cos cos sin sin cos( ) = cos cos + sin sin sin( + ) = sin cos + cos sin sin( ) = sin cos cos sin Other Formulas: cos(/2 ) = sin sin(/2 ) = cos 6.5 Double-Angle Formulas: sin(2) = 2 sin cos cos(2) = cos sin cos(2) = 1 2 sin cos(2) = 2 cos 1 tan(2) = 2 tan 1 - tan where where where where where where -1 < x < 1 and -/2 < y < /2 -1 < x < 1 and 0<y< - < x < and -/2 < y < /2 |x| > 1 and |x| > 1 and - < x < and 0<y<, - /2 < y < /2 , 0<y< y /2 y0 Pythagorean Identities: sin + cos = 1 tan + 1 = sec cot + 1 = csc tan( + ) = tan + tan 1 tan tan tan( ) = tan tan 1 + tan tan Double-Angle Variations: sin = 1 cos(2) 2 cos = 1 + cos(2) 2 tan = 1 cos(2) 1 + cos(2) Half-Angle Formulas: sin /2 = 1 cos 2 cos /2 = 1 + cos 2 tan /2 = 1 cos 1 + cos Half-Angle Variations: sin /2 = 1 cos 2 cos /2 = 1 + cos 2 tan /2 = 1 cos 1 + cos deg. -180 -150 -135 -120 -90 -60 -45 -30 0 30 45 60 90 120 135 150 180 rad. 5/6 3/4 2/3 -/2 -/3 -/4 -/6 0 /6 /4 /3 /2 2/3 3/4 5/6 sin 0 - -2/2 -3/2 -1 -3/2 -2/2 - 0 2/2 3/2 1 3/2 2/2 0 cos -1 -3/2 -2/2 - 0 2/2 3/2 1 3/2 2/2 0 - -2/2 -3/2 -1 tan 0 -3/3 -1 -3 undef. -3 -1 -3/3 0 3/3 1 3 undef. -3 -1 -3/3 0 ...
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Math Notes - Math Notes 6.1 y = sin-1 x x = sin y y = cos-1...

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