Given that sin 8^∘≈ 0.1392, cos 8^∘≈ 0.9903 tan 8^∘≈ 0.1405, cot 8^∘≈ 7.1154

Name: Problem 98, Chapter 6: Algebra and Trigonometry
Uploaded: 2020-07-13T18:16:17-08:00
Duration: 2 min 50 s
Channel: Ankit Gupta
Description: Given that sin 8^∘≈ 0.1392, cos 8^∘≈ 0.9903 tan 8^∘≈ 0.1405, cot 8^∘≈ 7.1154 sec 8^∘≈ 1.0098, csc 8^∘≈ 7.1853 find the six function values of 82^∘ .

step 1 In this question, we have to find the six function values of 82 degrees. We start with sine 82.

Question

Given that $$\begin{array}{ll} \sin 8^{\circ} \approx 0.1392, & \cos 8^{\circ} \approx 0.9903 \\ \tan 8^{\circ} \approx 0.1405, & \cot 8^{\circ} \approx 7.1154 \\ \sec 8^{\circ} \approx 1.0098, & \csc 8^{\circ} \approx 7.1853 \end{array}$$ find the six function values of $82^{\circ} .$

   Given that
$$\begin{array}{ll}
\sin 8^{\circ} \approx 0.1392, & \cos 8^{\circ} \approx 0.9903 \\
\tan 8^{\circ} \approx 0.1405, & \cot 8^{\circ} \approx 7.1154 \\
\sec 8^{\circ} \approx 1.0098, & \csc 8^{\circ} \approx 7.1853
\end{array}$$
find the six function values of $82^{\circ} .$

Algebra and Trigonometry

Judith A. Beecher,… 4th Edition

Chapter 6, Problem 98

Instant Answer

Solved by Expert Ankit Gupta

07/13/2020

Step 1

Therefore, $\sin(82^{\circ}) = \cos(90 - 82^{\circ}) = \cos(8^{\circ})$. Given that $\cos(8^{\circ}) \approx 0.9903$, we find that $\sin(82^{\circ}) \approx 0.9903$. Show more…

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Given that $$\begin{array}{ll} \sin 8^{\circ} \approx 0.1392, & \cos 8^{\circ} \approx 0.9903 \\ \tan 8^{\circ} \approx 0.1405, & \cot 8^{\circ} \approx 7.1154 \\ \sec 8^{\circ} \approx 1.0098, & \csc 8^{\circ} \approx 7.1853 \end{array}$$ find the six function values of $82^{\circ} .$

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Key Concepts

Co-function Identities

Co-function identities reveal that the trigonometric function of an angle is equal to the co-function of its complement. In particular, expressions like sin(?) = cos(90° - ?) and tan(?) = cot(90° - ?) allow one to compute the values of trigonometric functions for complementary angles, which is essential in problems where one angle's function is derived from another's.

Reciprocal Identities

Reciprocal identities establish that certain trigonometric functions are the inverses of others. For example, secant is the reciprocal of cosine, and cosecant is the reciprocal of sine. These identities allow the computation of functions such as sec, csc, and cot if their corresponding primary functions (cos, sin, and tan) are known.

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