At 270 degrees, which is equivalent to
3π/2 radians, we can determine the values of the six primary trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent.
1. Sine Function
The sine of 270 degrees is given by:
sin(270°) = -1
2. Cosine Function
The cosine of 270 degrees is:
cos(270°) = 0
3. Tangent Function
tan(270°) = sin(270°) / cos(270°) = -1 / 0Therefore, tangent is undefined at this angle.
4. Cosecant Function
The cosecant is the reciprocal of sine:
csc(270°) = 1 / sin(270°) = 1 / -1 = -1
5. Secant Function
The secant is the reciprocal of cosine:
sec(270°) = 1 / cos(270°) = 1 / 0
Consequently, secant is also undefined at this angle.
6. Cotangent Function
The cotangent is the reciprocal of tangent:
cot(270°) = 1 / tan(270°)
Given that tangent is undefined, cotangent is also undefined at 270 degrees.
In summary, the values for trigonometric functions at 270 degrees are as follows:
sin(270°) = -1cos(270°) = 0tan(270°) = undefinedcsc(270°) = -1sec(270°) = undefinedcot(270°) = undefined
Understanding these values can help in various applications of trigonometry, such as solving equations or analyzing wave behavior.