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This is going to require some visualization. Cosine is defined as the x-value on the unit circle.
If you picture where a point would be, for example, at the angle of pi/6 (30°) you get a coordinate of (√(3)/2 , 1/2) so cosine is √(3)/2 and sine is 1/2
To find a negative angle you take the reflection across the x-axis. Since this does not chance the x-value, only the y, cosine does not change. The coordinates of -(pi/6) (-30°) are (√(3)/2 , -1/2).
cos(-x) = cos(x)
sin(-x) = - sin(x)■
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What does sine times cosine equal?
Sin(x) cos(x) = 1/2 of sin(2x)
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.
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.
What is the formula for the y-intercept of a cosine function?
The Y-Intercept of the cosine function is X = 0, Y = cosine(0) = 1.
Why the value of cos positive for negative value of angle?
The cosine of an angle is the adjacent side of the angle of a triangle divided the hypotenuse. If you plot the adjacent side as x on an x -y graph, for negative angles less than 90 degrees the adjacent side is positive and the hypotenuse is always positive, so you get a positive. The cosine is positive int e upper right and lower right quadrants
