In what quadrant is secant negative and tangent positive?IVIIIIII
Question
In what quadrant is secant negative and tangent positive?IVIIIIII
Solution
To determine the quadrant in which secant is negative and tangent is positive, we can refer to the mnemonic "All Students Take Calculus" (ASTC) to remember the signs of trigonometric functions in each quadrant.
In the ASTC mnemonic, the first letter of each word represents the sign of the trigonometric functions in the corresponding quadrant. Starting from the positive x-axis and moving counterclockwise, the signs are as follows:
- Quadrant I: All functions are positive.
- Quadrant II: Sine is positive.
- Quadrant III: Tangent is positive.
- Quadrant IV: Cosine is positive.
Since we are looking for a quadrant where secant is negative and tangent is positive, we can conclude that it is Quadrant III.
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