Table of Contents
In which quadrant is sine positive and cosine negative?
Explanation: Trigonometric functions sine and cosine are both positive in first quadrant but in third quadrant both are negative. Hence in these two quadrants they have same sign. However, in second quadrant while sine is positive, cosine is negative.
What angle has a negative sine and a positive cosine?
| θ | sin θ | cos θ |
|---|---|---|
| 90° | 1 | 0 |
| 180° | 0 | −1 |
| 270° | −1 | 0 |
| 360° | 0 | 1 |
In what quadrant does an angle lie if the sine of the angle is negative and the cosine is positive?
Quadrant II
Quadrant I: sine, cosine, and tangent are positive. Quadrant II: sine is positive (cosine and tangent are negative). Quadrant III: tangent is positive (sine and cosine are negative).
Which quadrant is cosine positive?
Quadrant 4
Sine and cosecant are positive in Quadrant 2, tangent and cotangent are positive in Quadrant 3, and cosine and secant are positive in Quadrant 4.
Why is the cosine of a negative angle positive?
Why does cos change a negative angle into a positive? – Quora. A positive angle conventionally means anticlockwise direction and a negative angle means clockwise direction. Consider the following: Since the angle makes with is anticlockwise, it is taken as positive and the other is clockwise, so it is taken as negative …
Is negative cosine equal to cosine?
Comparing Cosine functions Compare equations of both cosine of positive angle and cosine of negative angle. The two equations reveals that cosine of negative angle is always equal to cosine of angle. It is called cosine of negative angle identity and often used as a formula in trigonometric mathematics.
Can cosine be negative?
However, as we are in the third quadrant, cosine must be negative! Therefore, our true cosine is. .
In what quadrants is sine negative?
The sine ratio is y/r, and the hypotenuse r is always positive. So the sine will be negative when y is negative, which happens in the third and fourth quadrants.
What quadrants is sine negative?
Is cosine negative or positive?
In the fourth quadrant cos (CUPS) values are positive while, sine and tan are negative. In all the four quadrants, the angle is measured with respect to the x-axis. Remember All Silver Tea Cups. In the first quadrant all (ALL) the values – sine, cos and tan are positive.
Is cosine equal to negative sine?
A similar reasoning based on the sine law makes it clear that the sine of an obtuse angle should be the same as the sine of the supplementary angle. just by looking at the trigonometric circle. cos(−θ)=cos(0−θ)=cos0cosθ+sin0sinθ=cos(θ). sin(−θ)=sin(0−θ)=sin0cosθ−cos0sinθ=−sin(θ).
Why cosine of negative angle is positive?
Δ Q O P is a right angled triangle, constructed with an angle theta. Write cosine of angle in terms of ratio of lengths of the sides. Δ Q O P is constructed in first quadrant. So, the lengths of adjacent and opposite sides are positive.
Is cosine negative or positive quadrant 3?
In Quadrant III, sine and cosine are negative: Example: The sine, cosine and tangent of 210° Note: Tangent is positive because dividing a negative by a negative gives a positive. In Quadrant IV, sine and tangent are negative:
How do you find the cosine of an angle in fourth quadrant?
For an angle in the fourth quadrant the point P has positive x coordinate and negative y coordinate. Therefore: In Quadrant IV, cos (θ) > 0, sin (θ) < 0 and tan (θ) < 0 (Cosine positive). The quadrants in which cosine, sine and tangent are positive are often remembered using a favorite mnemonic.
Why sine and tangent are negative in Quadrant 4?
Finally, when angle a is in Quadrant 4 (between 270° and 360°), the adjacent side is back along the positive x- direction, while the opposite side is still in the positive y- direction. Hence, Sine and Tangent are negative and only Cosine ( C) is positive.
How do you find the sin of an angle in Quadrant 2?
For an angle in the second quadrant the point P has negative x coordinate and positive y coordinate. Therefore: In Quadrant II, cos (θ) < 0, sin (θ) > 0 and tan (θ) < 0 (Sine positive). For an angle in the third quadrant the point P has negative x and y coordinates.