How do you find the value of Quadrantal angles?
Once you have an angle θ with 0° ≤ θ ≤ 360°, you can find its reference angle as follows:
- If the terminal ray of θ lies in quadrant I, then θ ‘ = θ.
- If the terminal ray of θ lies in quadrant II, then θ ‘ = 180° − θ.
- If the terminal ray of θ lies in quadrant III, then θ ‘ = θ − 180° .
What Quadrantal angles will result in undefined trigonometric functions?
If angle θ is a quadrantal angle, then either x or y will be 0, yielding the undefined values if the denominator is zero. The sign, positive or negative, of the trigonometric functions depends on which quadrant this point A (x, y) is located in. Table 1 summarizes this information.
How do you evaluate csc 3pi 2?
The value of csc 3pi/2 can be calculated by constructing an angle of 3π/2 radians with the x-axis, and then finding the coordinates of the corresponding point (0, -1) on the unit circle. The value of csc 3pi/2 is equal to the reciprocal of the y-coordinate (-1). ∴ csc 3pi/2 = -1.
What trig functions are undefined for Quadrantal angles?
FINDING FUNCTION VALUES OF QUADRANTAL ANGLES If the terminal side of a quadrantal angle lies along the x-axis, then the cotangent and cosecant functions are undefined.
What are Quadrantal angles?
A quadrantal angle is one that is in the standard position and has a measure that is a multiple of 90° (or π/2 radians). A quadrantal angle will have its terminal lying along an x or y axis.
How do you evaluate a trig using the unit circle?
The way the unit circle works is to draw a line from the center of the circle outwards corresponding to a given angle. Then look at the coordinates of the point where the line and the circle intersect. The first coordinate is the cosine of that angle and the second coordinate is the sine of that angle.
How do you know if a trig function is undefined?
Correct answer: Trigonometric functions are undefined when they represent fractions with denominators equal to zero. Secant is the reciprocal of cosine, so the secant of any angle x for which cos x = 0 must be undefined, since it would have a denominator equal to 0.
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.
How do you evaluate csc?
To evaluate the cosecant, secant, and cotangent functions, use the x-1 key with their respective reciprocal functions sine, cosine, and tangent. For example to evaluate csc (π / 8), first find the sin (π / 8), then use the x-1 key to find its reciprocal.
