Final answer:
Subtracting by 180 degrees is not a step associated with finding the sine, cosecant, cotangent, or secant of an angle. This operation is typically used to adjust angles in the third or fourth quadrant to their corresponding acute angles in the unit circle for the tangent function, which is periodic with a period of 180°.
Step-by-step explanation:
You asked about when to subtract by 180 when using tangent. In trigonometry, particularly when solving for angles or when working with the functions of angles in different quadrants, you may need to use certain adjustments to find the correct angle. However, the subtraction by 180 is not applicable to the options provided, which are finding sine (A), cosecant (B), cotangent (C), or secant (D). Instead, subtracting by 180 degrees typically comes into play when adjusting an angle from the third or fourth quadrant to its corresponding acute angle in the first quadrant. This adjustment reflects the periodic nature of the tangent function, where tangent of an angle θ is equal to tangent of (θ ± 180°) for any angle θ.
For example, if the tangent function gives you an angle in the third quadrant, and you are trying to find the related acute angle, you would subtract 180 degrees to obtain the positive acute angle in the first quadrant. This would give you the reference angle for your original angle. It is important to remember that tangent, sine, and cosine are periodic functions with specific periods (180° for tangent and cotangent, 360° for sine and cosine), and they will repeat values over their cycles.
To accurately work with trigonometric functions and find the correct values for angles, you must understand the unit circle, where each trigonometric function has specific values at various angles. Therefore, the correct answer to the question would be 'none of the above', as subtracting by 180 degrees is not a routine step in finding sine, cosecant, cotangent, or secant.
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