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Trigonometry And Coordinate
MODULES
PRACTICE
The first letters of the words “All Silver Tea Cups”, i.e. A, S, T and C signify the trigonometric functions that would be positive across the 4 quadrants in that order, i.e. All, Sin, Tan and Cos. ('All' means all the trigonometric functions, i.e., Sin, Tan, Cos, etc.) As cosecθ=sinθ1, secθ=cosθ1 and cotθtanθ1, these functions will also have the same sign (positive/negative) as their respective reciprocal functions. The table below summarises this. |
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Quadrant | Range | Positive Ratios | Negative Ratios |
---|---|---|---|
Quadrant 1 | 0° to 90° | All (Sin, Cosec, Tan, Cot, Cos, Sec) | - |
Quadrant 2 | 90° to 180° | Sin, Cosec | Cos, Sec, Tan, Cot |
Quadrant 3 | 180° to 270° | Tan, Cot | Sin, Cosec, Cos, Sec |
Quadrant 4 | 270° to 360° | Cos, Sec | Sin, Cosec, Tan, Cot |
Steps | Example: Sin 240° |
---|---|
1) Find the multiples of 90 between which the angle is. You can use any one of these to get the answer. | 180° and 270° |
2) Write the angle with respect to the multiple of 90° | Sin (180° + 60°) (270° - 30°) |
3) Value will be positive/negative depending on the angle (i.e. 240°) and the function (i.e., Sin) for which the value needs to be found (in this case negative as Sin is negative in Quadrant 3). 4) If an odd multiple of 90° is used, then switch the functions (as stated above). Retain the function if it is an even multiple of 90. (180 is an even multiple, while 270 is an odd multiple of 90) |
- Sin 60° - Cos 30° |
5) Write down the final answer | 2−3 2−3 |
Functions | Range |
---|---|
Sin x and Cos x | [-1, 1] |
Tan x and Cot x | (-∞, +∞) |
Sec x and Cosec x | (-∞, -1] ∪ [1, +∞) |
Graph for f(x)=sinx | ![]() |
Graph for f(x)=cosx | ![]() |
Graph for f(x)=tanx | ![]() |
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