Evaluate, correct to 4 significant figures: (a) cosecant...

Evaluate, correct to 4 significant figures: (a) cosecant $279.16$ (b) cosecant $49^{\circ} 7^{\prime}$ (a) $\operatorname{cosec} 279.16^{\circ}=\frac{1}{\sin 279.16^{\circ}}=-\mathbf{1 . 0 1 3}$ (b) $\quad \operatorname{cosec} 49^{\circ} 7^{\prime}=\frac{1}{\sin 49^{\circ} 7^{\prime}}=\frac{1}{\sin 49 \frac{7^{\circ}}{60}}$ $=\mathbf{1 . 3 2 3}$

Evaluate, correct to 4 significant figures:
(a) cosecant $279.16$
(b) cosecant $49^{\circ} 7^{\prime}$
(a) $\operatorname{cosec} 279.16^{\circ}=\frac{1}{\sin 279.16^{\circ}}=-\mathbf{1 . 0 1 3}$
(b) $\quad \operatorname{cosec} 49^{\circ} 7^{\prime}=\frac{1}{\sin 49^{\circ} 7^{\prime}}=\frac{1}{\sin 49 \frac{7^{\circ}}{60}}$ $=\mathbf{1 . 3 2 3}$

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Key Concepts

Reciprocal Trigonometric Functions

In trigonometry, the reciprocal functions are defined as the inverses of the standard trigonometric functions. For example, the cosecant function is defined as the reciprocal of the sine function (cosec ? = 1/sin ?). This concept is crucial when solving problems where the evaluation of a trigonometric function requires using its reciprocal identity, often simplifying the computation process.

Angle Measurement and Conversion

Trigonometric calculations often involve angles given in various formats such as degrees, minutes, and seconds. Converting these measurements into a consistent format, typically decimal degrees, is essential for accurate computation. Understanding and executing this conversion allows one to correctly evaluate trigonometric functions using standard calculators or mathematical methods.

Significant Figures and Rounding

Significant figures provide a way to express the precision of a numerical result. In problems requiring answers to a specific number of significant figures, it is important to perform calculations with sufficient accuracy and then correctly round the result to meet the specified precision. This concept ensures that numerical answers reflect the inherent limitations of the data or computation methods used.

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