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Question: How do you use a calculator to evaluate \( \sec {79.3^ \circ } \) ?...

How do you use a calculator to evaluate sec⁡79.3∘\sec {79.3^ \circ } ?

Explanation

Solution

Hint : To solve this question we should know about trigonometric identity:
Trigonometry: It is the study of the relationship between side length and angle of triangle.
Trigonometry ratio:
A. sin⁡θ=prependiucalrhypotenius\sin \theta = \dfrac{{prependiucalr}}{{hypotenius}}
B. cos⁡θ=basehypotenius\cos \theta = \dfrac{{base}}{{hypotenius}}
C. tan⁡θ=prependiucalrbase\tan \theta = \dfrac{{prependiucalr}}{{base}}
D. sec⁡θ=1cos⁡θ\sec \theta = \dfrac{1}{{\cos \theta }}
E. cos⁡ecθ=1sin⁡θ\cos ec\theta = \dfrac{1}{{\sin \theta }}

Complete step by step solution:
As we have to calculate sec⁡79.3∘\sec {79.3^ \circ } .
We know that sec⁡x=1cos⁡x\sec x = \dfrac{1}{{\cos x}}
So,
sec⁡79.3∘=1cos⁡79.3∘\sec {79.3^ \circ } = \dfrac{1}{{\cos {{79.3}^ \circ }}}
From a calculator, in degree mode:
1cos⁡79.3∘=10.1856666154\dfrac{1}{{\cos {{79.3}^ \circ }}} = \dfrac{1}{{0.1856666154}}
=5.385997897= 5.385997897
We can write it as,
=5.3860(4dp)= 5.3860(4dp) apporx
If you have a calculator such as Casio fx−83ESfx - 83ES you can type
1cos⁡79.3∘\dfrac{1}{{\cos {{79.3}^ \circ }}}
Directly press = and get the answer immediately without using the reciprocal key.

Note : Trigonometry is used in civil engineering, architecture, measurement of unknown height and many more things.
There are some trigonometry identity:
sin⁡2θ+cos⁡2θ=1{\sin ^2}\theta + {\cos ^2}\theta = 1
1+tan⁡2θ=sec⁡2θ1 + {\tan ^2}\theta = {\sec ^2}\theta
1+cot⁡2θ=cos⁡ec2θ1 + {\cot ^2}\theta = \cos e{c^2}\theta
There are some other identity:
tan⁡θ=sin⁡θcos⁡θ\tan \theta = \dfrac{{\sin \theta }}{{\cos \theta }}
cot⁡θ=cos⁡θsin⁡θ=1tan⁡θ\cot \theta = \dfrac{{\cos \theta }}{{\sin \theta }} = \dfrac{1}{{\tan \theta }}