Trigonometry
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Trigonometry
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Lesson 3 Precalculus Online
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Lesson 3: Trigonometric Functions Topic 3: Reference Angles Examples : Find the reference angle for each angle. 1. Find the reference angle for 218?. Find the positive acute angle made by the terminal side of the angle and the x-axis: The reference angle for 218? is 218? - 180? = 38? 2. Find the reference angle for 1387 ? First find a coterminal angle between 0? and 360?. Divide 1387 by 360 to get a quotient of about 3.9. So subtract 360 three times. 1387? ? 3(360? ) = 307?. The reference angle for 307 ? is 360? ? 307? = 53? 360? ? 307? = 53? 3. Find the reference angle for -237? Find a coterminal positive angle by adding 360?: -237? + 360? = 123? The reference angle for 123? is 180? - 123? = 57?. 180 ? ? 123 ? = 57 ? 180? ? 123? = 57? Practice
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Precalculus - Trignometry Cheat sheet
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? 2005 Paul Dawkins Trig Cheat Sheet Definition of the Trig Functions Right triangle definition For this definition we assume that 0 2 pq< < or 0 90q? < < ? . oppositesin hypotenuseq = hypotenusecsc oppositeq = adjacentcos hypotenuseq = hypotenusesec adjacentq = oppositetan adjacentq = adjacentcot oppositeq = Unit circle definition For this definition q is any angle. sin 1 y yq = = 1csc yq = cos 1 x xq = = 1sec xq = tan yxq = cot x yq = Facts and Properties Domain The domain is all the values of q that can be plugged into the function. sinq , q can be any angle cosq , q can be any angle tanq , 1 , 0, 1, 2,2n nq p ? ?? + = ? ?? ?? ? K cscq , , 0, 1, 2,n nq p? = ? ? K secq , 1 , 0, 1, 2,2n nq p
Trig cheat sheet
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? 2005 Paul Dawkins Trig Cheat Sheet Definition of the Trig Functions Right triangle definition For this definition we assume that 0 2 pq< < or 0 90q? < < ? . oppositesin hypotenuseq = hypotenusecsc oppositeq = adjacentcos hypotenuseq = hypotenusesec adjacentq = oppositetan adjacentq = adjacentcot oppositeq = Unit circle definition For this definition q is any angle. sin 1 y yq = = 1csc yq = cos 1 x xq = = 1sec xq = tan yxq = cot x yq = Facts and Properties Domain The domain is all the values of q that can be plugged into the function. sinq , q can be any angle cosq , q can be any angle tanq , 1 , 0, 1, 2,2n nq p ? ?? + = ? ?? ?? ? K
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Log equations
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Trig exponents worksheet
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Trig
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10.5 Notes - Rotation of Axes At times we may be faced with an equation of a conic section whose axes would not be parallel to the x or y-axes. (These conics have an equation of the form where .) As a result it may be difficult to ascertain the nature of the graph or its position on the coordinate system. In this case we may simplify the equation by a process of rotating the axes. ? In the figure the axes have been rotated through an acute angle about the origin to produce a new pair of axes, which we will call the X and Y axes. A point P that has coordinates (x, y) in the old system has coordinates (X,Y) in the new system. Let r equal the distance of P from the origin. Let be the angle that segment OP makes with the X axis. ? ?
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