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# Signs of trigonometric ratios

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This presentation illustrate the use of signs of trigonometric ratios

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### Signs of trigonometric ratios

1. 1. Signs of trigonometric ratios by SBR www.harekrishnahub.com
2. 2. www.harekrishnahub.com Consider a circle with centre πΆ and radius π units. Let the circle cut the π β ππππ at π¨ and π¨β² and π β ππππ at π© and π©β². Let π· (π, π) be any point on the circumference of the circle. Join πΆπ·. Let the radius vector πΆπ· make an angle π½ with the positive π β ππππ. β΄ β πΏπΆπ· = π½ and πΆπ· = π Draw π·π΄ β to the π β ππππ. β΄ πΆπ΄ = π and π·π΄ = π
3. 3. www.harekrishnahub.com β΄ we have, Points Coordinates π π₯, π¦ π π₯, 0 π΄ π, 0 π΅ 0, π π΄β² βπ, 0 π΅β² 0, βπ
4. 4. www.harekrishnahub.com βΏπ·π΄πΆ form a right angle triangle. We have, πππ π½ = π π ππ π π½ = π π πππ π½ = π π π represents the magnitude (length) of the radius vector πΆπ·. It is always positive. πΆπ΄ and π·π΄ represents the horizontal and vertical displacement components of point π·. Hence, they can be positive or negative depending the quadrant in which the radius vector πΆπ· lies.
5. 5. www.harekrishnahub.com Quadran t π Sign Trigonometric ratios Remarks π₯ π¦ π ππ π = π¦ π πππ  π = π₯ π π‘ππ π = π¦ π₯ I 0 < π < 90 + + + + = + π£π + + = + π£π + + = + π£π ALL +ve II 90 < π < 180 - + + + = + π£π β + = β π£π + β = β π£π SIN +ve III 180 < π < 270 - - β + = β π£π β + = β π£π β β = + π£π TAN +ve IV 270 < π < 360 + - β + = β π£π + + = + π£π β + = β π£π COS +ve
6. 6. www.harekrishnahub.com β’ Thus, in the first quadrant, all of the trigonometric ratios are positive. β’ In the second quadrant, only πππ π½ and πππππ π½ are positive and all other ratios are negative. β’ In the third quadrant, only tan π½ and cot π½ are positive and all other ratios are negative. β’ In the fourth quadrant, only cos π½ and sec π½ are positive and all other ratios are negative.
7. 7. www.harekrishnahub.com The following figure is useful in remembering the signs of the trigonometric ratios.
8. 8. www.harekrishnahub.com When P Coincides with π₯ π¦ π ππ π π¦ π πππ  π π₯ π π‘ππ π π¦ π₯ π¨ (π½ = π) π 0 π ππ 0 = 0 πππ  0 = 1 π‘ππ 0 = 0 π© π½ = ππ 0 π π ππ 90 = 1 πππ  90 = 0 π‘ππ 90 = β π¨β² π½ = πππ βπ 0 π ππ 180 = 0 πππ  180 = β1 π‘ππ 180 = 0 π©β² π½ = πππ 0 βπ π ππ 270 = β1 πππ  270 = 0 π‘ππ 270 = ββ