Question

write the function value in terms of the cofunction of a complementary angle tan 116°28 tan 116°28 = □ (□°□) (simplify your answers. type the cofunction abbreviation in the first input box. type the degree part of the angle measure in the second input box. type the minute part of the angle measure in the third input box.)

Explanation:

Step1: Recall the co - function identity

The co - function identity for tangent is \(\tan\theta=\cot(90^{\circ}-\theta)\) when \(\theta\) is an acute angle. But for \(\theta = 116^{\circ}28'\), we use the identity \(\tan\theta=-\cot(\theta - 90^{\circ})\)

Step2: Calculate the complementary - related angle

We have \(\theta=116^{\circ}28'\). Then \(\theta - 90^{\circ}=116^{\circ}28'-90^{\circ}\)

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Answer:

\(\tan116^{\circ}28'=-\cot(26^{\circ}28')\)