TRIG_TR4

This transformation identifies and evaluates trigonometric values at common special angles exactly, using symbolic constants.

Examples include:

\sin\left(\frac{\pi}{6}\right)=\frac{1}{2},\quad \cos\left(\frac{\pi}{3}\right)=\frac{1}{2}

It is useful for converting unevaluated trig calls at known angles into exact algebraic forms.

Excel Usage

=TRIG_TR4(expression)

• expression (str, required): Expression containing trig values at special angles (expression string).

Returns (str): Transformed expression as a string, or an error message.

Example 1: Evaluates sine at pi over six

Inputs:

expression
sin(pi/6)

Excel formula:

=TRIG_TR4("sin(pi/6)")

Expected output:

"1/2"

Example 2: Evaluates cosine at pi over four

Inputs:

expression
cos(pi/4)

Excel formula:

=TRIG_TR4("cos(pi/4)")

Expected output:

"sqrt(2)/2"

Example 3: Evaluates tangent at pi over three

Inputs:

expression
tan(pi/3)

Excel formula:

=TRIG_TR4("tan(pi/3)")

Expected output:

"sqrt(3)"

Example 4: Evaluates a sum of special-angle trig terms

Inputs:

expression
cos(pi/3) + sin(pi/6)

Excel formula:

=TRIG_TR4("cos(pi/3) + sin(pi/6)")

Expected output:

"1"

Python Code

from sympy import sympify
from sympy.simplify.fu import TR4 as sympy_tr4

def trig_tr4(expression):
    """
    Evaluate exact trigonometric values at standard special angles.

    See: https://docs.sympy.org/latest/modules/simplify/fu.html#sympy.simplify.fu.TR4

    This example function is provided as-is without any representation of accuracy.

    Args:
        expression (str): Expression containing trig values at special angles (expression string).

    Returns:
        str: Transformed expression as a string, or an error message.
    """
    try:
        expr_text = expression.replace("^", "**") if isinstance(expression, str) else expression
        expr_obj = sympify(expr_text)
        result = sympy_tr4(expr_obj)
        return str(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

expression *

Expression containing trig values at special angles (expression string).