Purpose
Return value
Syntax
=RADIANS(angle)
- angle - Angle in degrees to convert to radians.
Using the RADIANS function
The RADIANS function takes an angle in degrees and converts it to radians. Radians measure angles using the radius of a circle. For example, to convert a 45 degree angle to radians the formula is:
=RADIANS(45) // Returns 0.785 or π/4
Explanation
One radian is equal to the amount of rotation required to travel one radius along the circumference of the circle, as seen in the image above. A full-rotation or 360° in radians is equal to the value of 2π. A half-rotation or 180° in radians is equal to the value of geometric constant π (pi) .
= RADIANS(360) =2*PI() // A full rotation is 6.283...
= RADIANS(180) =PI() // A half rotation is 3.141...
Notes
- To convert radians to degrees, see the DEGREES function .
- A full-rotation (360°) in radians is equal to 6.283 or 2π
- A half-rotation (180°) in radians is equal to 3.142 or π (pi).
Purpose
Return value
Syntax
=SEC(number)
- number - The angle in radians for which you want the secant.
Using the SEC function
The SEC function returns the secant of an angle provided in radians . In geometric terms, the secant of a right-triangle’s angle is equal to the ratio of the length of its hypotenuse over the length of its adjacent side. For example, the secant of PI()/6 (30°) returns the ratio 1.514.
=SEC(PI()/6) // Returns 1.514
Using Degrees
To supply an angle to SEC in degrees, multiply the angle by PI()/180 or use the RADIANS function to convert to radians. For example, to get the COT of 60 degrees, you can use either formula below:
=SIN(60*PI()/180)
=SIN(RADIANS(60))
Explanation
The graph of SEC, shown above, visualizes the output of the function for angles from 0 to a full rotation. The function has two vertical asymptotes at π/2 and 3π/2 respectively where the output of the function diverges to infinity. The SEC function is the reciprocal of COS and can be equivalently defined in the formula below:
=SEC(angle)=1/COS(angle)
The relationship between SEC and COS is visualized in the graph of both of the functions shown below:
Images courtesy of wumbo.net .
