Where is cosine and secant positive?

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 sin and cos are positive in 2nd quadrant?

The angles between 90° and 180° are in the second quadrant, angles between 180° and 270° are in the third quadrant and angles between 270° and 360° are in the fourth quadrant: In the first quadrant, the values for sin, cos and tan are positive. In the second quadrant, the values for sin are positive only.

Is secant positive or negative?

In quadrant II, “Smart,” only sine and its reciprocal function, cosecant, are positive. In quadrant III, “Trig,” only tangent and its reciprocal function, cotangent, are positive. Finally, in quadrant IV, “Class,” only cosine and its reciprocal function, secant, are positive.

How do you know if a trig function is positive or negative?

Signs of Angles in Quadrants The distance from a point to the origin is always positive, but the signs of the x and y coordinates may be positive or negative. Thus, in the first quadrant, where x and y coordinates are all positive, all six trigonometric functions have positive values.

Why is Secant negative quadrant 3?

Since r is a radius, it must be positive, so sec(x) is negative anywhere x is negative.

Is secant always positive?

Signs of Angles in Quadrants Thus, in the first quadrant, where x and y coordinates are all positive, all six trigonometric functions have positive values. In the second quadrant, only sine and cosecant (the reciprocal of sine) are positive. Finally, in the fourth quadrant, only cosine and secant are positive.

Is secant the reciprocal of cosine?

The secant is the reciprocal of the cosine. It is the ratio of the hypotenuse to the side adjacent to a given angle in a right triangle.

Why is cosine always positive?

The short answer is because cosine is an even function; it has y-axis symmetry. To see why this is so, let an angle have a measure of x degrees (or radians; it doesn’t matter here) and suppose, purely for convenience, that x is positive.

Can cosine be negative?

However, as we are in the third quadrant, cosine must be negative! Therefore, our true cosine is. .