Chapter 66, Problem 1A

If cos 35°18', write the cofunction of the complement of the angle.

To determine

The cofunction of cos $35°18^{\prime }$.

Answer to Problem 1A

The required value is, sin $54°{42}^{\prime }$.

Explanation of Solution

Given information:

Cos $35°18^{\prime }$

Calculation:

First convert the angle in decimal form.

  $\begin{array}{l}\cos 35°18^{\prime }\\ \Rightarrow \cos 35°18^{\prime }\\ \Rightarrow \cos \left(35°+\frac{18}{60}\right)=\cos \left(35°+0.3°\right)=\cos \left(35.3°\right)\end{array}$

We need to find the cofunction of cos35.3⁰.

  $\begin{array}{l}\cos 35°18^{\prime }\\ \Rightarrow \cos 35°18^{\prime }\\ \Rightarrow \cos \left(35°+\frac{18}{60}\right)\\ =\cos \left(35°+0.3°\right)\\ =\cos \left(35.3°\right)\\ \because \cos \left(90°-\theta \right)=\sin \theta \\ \therefore \cos \left(90°-35.3°\right)=\sin 54.7°\end{array}$

Converting the angles into minutes,

  $\begin{array}{l}=54.7°\\ =54°+\left(0.7\times 60\right)\\ =54°+{\left(42\right)}^{\prime }\\ =54°+{42}^{\prime }\\ =54°{42}^{\prime }\end{array}$

The required value is sin $54°{42}^{\prime }$.