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Why is the tangent positive on quadrant III?
The tangent function is equal to the sine divided by the cosine. In quadrant III, both sin and cos are negative - and a negative divided by another negative is positive. Thus it follows that the tangent is positive in QIII.
Is the cosine function an odd function?
No. Cosine, along with sec, is an even function. The odd functions are sin, tan, csc, and cot. The reason for this is because is you take the opposite of the y-value for the cosine function, the overall value of the function is not affected.Take, for example, cos(60 degrees), which equals POSITIVE 1/2.If you flip it over the x-axis, making the y's negative, it becomes cos(-60 degrees), or cos(300 degrees). This equals POSITIVE 1/2.Now let's look at an odd function. For example, sin(30 degrees) equals POSITIVE 1/2. Now take the opposite of this.sin(-30 degrees), or sin(330 degrees), equals NEGATIVE 1/2. This is because it is found in the fourth quadrant, where the y's are negative. Sine of theta, by definition, is y divided by r. If y is negative, sine is negative.
What is the difference between negative sine and cosine graphs and positive sine and cosine graphs?
The negative sine graph and the positive sine graph have opposite signs: when one is negative, the other is positive - by exactly the same amount. The sine function is said to be an odd function. The two graphs for cosine are the same. The cosine function is said to be even.
Rule for multiplying integers?
Positive x negative = negative (Negative x positive = negative) Positive x positive = positive Negative x negative = positive So if the signs are the same the answer is positive and if they are different it is negative.
What is the limit of trigonometric function csc 2x cos 5x as x tends to zero?
The answer depends on the side from which x approaches 0. If from the negative side, then the limit is negative infinity whereas if from the positive side, it is positive infinity.
Why will sin and cosecant have the same sign?
The cosecant is the reciprocal of the sine function. Now, the reciprocal of a positive number is positive, and the reciprocal of a negative number is negative.
What is sine of a negative angle?
The sine of a negative angle is equal to the negative sine of the corresponding positive angle. This is expressed mathematically as (\sin(-\theta) = -\sin(\theta)). This property reflects the odd function nature of the sine function, which means that its graph is symmetric about the origin. Therefore, if you know the sine of a positive angle, you can easily determine the sine of its negative counterpart.
Why is the tangent positive on quadrant III?
The tangent function is equal to the sine divided by the cosine. In quadrant III, both sin and cos are negative - and a negative divided by another negative is positive. Thus it follows that the tangent is positive in QIII.
Why does sin negative theta equal sin positive theta?
It is not! So the question is irrelevant.
Is the cosine function an odd function?
No. Cosine, along with sec, is an even function. The odd functions are sin, tan, csc, and cot. The reason for this is because is you take the opposite of the y-value for the cosine function, the overall value of the function is not affected.Take, for example, cos(60 degrees), which equals POSITIVE 1/2.If you flip it over the x-axis, making the y's negative, it becomes cos(-60 degrees), or cos(300 degrees). This equals POSITIVE 1/2.Now let's look at an odd function. For example, sin(30 degrees) equals POSITIVE 1/2. Now take the opposite of this.sin(-30 degrees), or sin(330 degrees), equals NEGATIVE 1/2. This is because it is found in the fourth quadrant, where the y's are negative. Sine of theta, by definition, is y divided by r. If y is negative, sine is negative.
Which quadrant would an answer be in if tan was positive and sin was negative?
The third quadrant.
Which the function's values become very positive or negative numbers?
The positive regions of a function are those intervals where the function is above the x-axis. It is where the y-values are positive (not zero). The negative regions of a function are those intervals where the function is below the x-axis. It is where the y-values are negative (not zero).
How does multiplying the sine function by a number less than zero affect the graph?
The same as multiplying any other function by a negative number - after multiplying, positive numbers will become negative numbers, and vice versa.
What does the absolute value function do?
It removes the negative from a negative number making it positive and it does nothing to a positive number or zero.
Are high beams positive or negative on 1997 crown Victoria?
They need both a positive connection and a negative connection to function.
What is cos of a negative angle?
The cosine function is an even function which means that cos(-x) = cos(x). So, if cos of an angle is positive, then the cos of the negative of that angle is positive and if cos of an angle is negative, then the cos of the negative of that angle is negaitive.
Why negative numbers don't have logarithim?
The logarithmic function is not defined for zero or negative numbers. Logarithms are the inverse of the exponential function for a positive base. Any exponent of a positive base must be positive. So the range of any exponential function is the positive real line. Consequently the domain of the the inverse function - the logarithm - is the positive real line. That is, logarithms are not defined for zero or negative numbers. (Wait until you get to complex analysis, though!)
