Evaluate, correct to 4 decimal places: (a) secant 5.37 (b) cosecant π/ 4 (c) cotangent π/ 24 (a)

step 1 in this question first secan 5 .37 so here 5 .37 means 5 .37 radiance so secant 5 .37 equal 1 by

Evaluate, correct to 4 decimal places: (a) secant 5.37 (b)...

Evaluate, correct to 4 decimal places: (a) secant $5.37$ (b) cosecant $\pi / 4$ (c) cotangent $\pi / 24$ (a) Again, with no degrees sign, it is assumed that $5.37$ means $5.37$ radians. Hence $\sec 5.37=\frac{1}{\cos 5.37}=1.6361$ (b) $\operatorname{cosec}(\pi / 4)=\frac{1}{\sin (\pi / 4)}=\frac{1}{\sin 0.785398 \ldots}$ $=1.4142$ (c) $\cot (5 \pi / 24)=\frac{1}{\tan (5 \pi / 24)}=\frac{1}{\tan 0.654498 \ldots}$ $=1.3032$

Evaluate, correct to 4 decimal places:
(a) secant $5.37$
(b) cosecant $\pi / 4$
(c) cotangent $\pi / 24$
(a) Again, with no degrees sign, it is assumed that $5.37$ means $5.37$ radians.
Hence $\sec 5.37=\frac{1}{\cos 5.37}=1.6361$
(b) $\operatorname{cosec}(\pi / 4)=\frac{1}{\sin (\pi / 4)}=\frac{1}{\sin 0.785398 \ldots}$ $=1.4142$
(c) $\cot (5 \pi / 24)=\frac{1}{\tan (5 \pi / 24)}=\frac{1}{\tan 0.654498 \ldots}$ $=1.3032$

Key Concepts

Radian Measure

Radian measure is a unit of angular measurement based on the radius of a circle, where one radian is the angle created when the arc length equals the radius. It is crucial in trigonometry since many formulas and functions assume angles are measured in radians rather than degrees, particularly in higher mathematics and calculus.

Reciprocal Trigonometric Functions

Reciprocal trigonometric functions are the inverses of the basic trigonometric functions. For example, secant is defined as the reciprocal of cosine, cosecant as the reciprocal of sine, and cotangent as the reciprocal of tangent. Understanding these definitions allows for the evaluation of these functions by dividing one by the corresponding trigonometric function.

Trigonometric Function Evaluation

Evaluating trigonometric functions involves computing the values of functions like sine, cosine, and tangent for specific angles. This process often requires using a calculator or tables, especially when the angles are given in radians or when the values are not commonly memorized.

Precision and Rounding

Precision and rounding refer to the process of adjusting a numerical result to a specified number of decimal places. In many problems, answers must be expressed to a particular degree of accuracy, such as to four decimal places, to maintain consistency and clarity in results.

Transcript

Please give Ace some feedback