Questions: Assignment 3.3: Values of Trigonometric Functions Question: Give each of the following trig values. Give exact answers only, using fractions and radicals. csc(π) tan(π/6) cos(π/3) sin(5π/6) sec(π/4) cot(π/3) myOpenMath Progress saved Submit and End

Solution Steps

To find the exact values of the given trigonometric functions, we will use the unit circle and known values of trigonometric functions at specific angles. The unit circle provides exact values for sine, cosine, tangent, and their reciprocals at key angles like π, π/6, π/3, π/4, and 5π/6.

The cosecant function is the reciprocal of the sine function. Since \(\sin(\pi) = 0\), \(\csc(\pi)\) is undefined. However, due to numerical limitations, the Python output shows a very large number, which indicates a division by a very small number close to zero.

The tangent of \(\pi/6\) is known to be \(\frac{1}{\sqrt{3}}\). The Python output approximates this as \(0.5774\).

The cosine of \(\pi/3\) is \(\frac{1}{2}\). The Python output approximates this as \(0.5000\).

The sine of \(5\pi/6\) is \(\frac{1}{2}\). The Python output approximates this as \(0.5000\).

The secant function is the reciprocal of the cosine function. Since \(\cos(\pi/4) = \frac{\sqrt{2}}{2}\), \(\sec(\pi/4) = \sqrt{2}\). The Python output approximates this as \(1.4142\).

The cotangent function is the reciprocal of the tangent function. Since \(\tan(\pi/3) = \sqrt{3}\), \(\cot(\pi/3) = \frac{1}{\sqrt{3}}\). The Python output approximates this as \(0.5774\).

Final Answer