Mathematics

Problem

For an acute angle

\theta

we have

\tan\theta = \dfrac{5}{12}

. Answer the following. a. (i) Find

\sec\theta

. b. (ii) Hence calculate

\cos\theta

correct to three decimal places. c. (iii) Using the values obtained, verify numerically that

\sin^{2}\theta + \cos^{2}\theta = 1

. Take

\sin\theta = \dfrac{5}{13}

for your verification.