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Created with Fabric.js 1.4.5 Trigonometric 3 4 5 A C B adjacent opposite hypotenuse sinA=opposite/hypotenusecosA=adjacent/hypotenusetanA=opposite/adjacentcsc=hypotenuse/oppositesec=hypotenuse/adjacentcotA=adjacent/opposte Trigonometric Ratios of Acute Angless 2 1 1 B A C 45˚ 45˚ 2 3 1 D F E 30˚ 60˚ A sinA cosA tanA 30˚ 45˚ 60˚ 1/2 2/2 3/2 3/2 2/2 1/2 3/3 1 3 Evaluating Trigonometric Ratios for Special Angles Exploring Trigonometric Ratios for Angles Greater than 90˚ x y sin(180˚-A)=sinAcos(180˚-A)=-cosAtan(180˚-A)=-tanA A A sin(180˚+A)=-sinAcos(180˚+A)=-cosAtan(180˚+A)=-tanA sin(360˚-A)=-sinAcos(360˚-A)=-cosAtan(360˚-A)=-tanA trigonometric Ratios for any angle between 0˚ and 360˚ 0˚ y x r x y P(x,y) from the pythagorean theorem and r >0sinA=y/r cosA=x/r tanA=y/xcsc=r/y sec=r/x cot=x/y A T C S A 2 1 4 3 x y o the CAST rule is an easy way to remember which primary trigonometric ratios are positive in which quadrant. Since r is always positive, the sign of each primary ratio depends on the signs of the coordinates of the point.-in quadrant 1, ALL (A)ratios are positive because both x and y are positive-in quadrant 2,only Sine(S) is positive, since x is negative and y is positive-in quadrant 3, only Tangent(T) is positive because both x and y are negative-in quadrant 4, only Cosine(C) is positive ,since x is positive and y is negative Trigonometric Identities The Sine Law c b A B c a a/sinA=b/sinB=c/sinC or sinA/a =sinB/b=sinC/c The ambiguous case arises in a SSA triangle. The sine law can lead to 0,1,2 situations Cosine Law aˆ2=bˆ2+ci2-2bcosAbˆ2=aˆ2+cˆ2-2accosBcˆ2=aˆ2+bˆ2-2abcosCcosA=(bˆ2+cˆ2-aˆ2)/2bccosB=(aˆ2+cˆ2-bˆ2)/2accosC=(aˆ2=+bˆ2-cˆ2)/2ab
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