Suppose that β is an acute angle and sec β = 11 . 3. How to do the following?

(a) Find the exact value of: (i) cosec β, (ii) cot β.

(b) Show that #co##sec^2# β − #cot^2# β = 1.

1 Answer
Nghi N
May 19, 2018

cosec b = 1.0039
cot b = 0.0888

Explanation:

#sec b = 11.3# -->
#cos b = 1/11.3 = 0.0885#. Find sin b.
#sin^2b = 1 - cos^2 b = 1 - 0.0078 = 0.9921#
#sin b = 0.9960#
cosec b = #1/(sin b) = 1.0039#
#cot b = cos b/(sin b) = 0.0085/(0.9960) = 0.0888#

#cosec^2 b - cot^2 b = 1.0078 - 0.0078 = 1#. Proved

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