A straight road rises for every horizontal run of

MATHEMATICS · Subjective · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

A straight road rises

3\,\text{m}

for every horizontal run of

8\,\text{m}

. The angle that the road makes with the horizontal is

\theta

, measured anticlockwise from the positive

x

–axis. (a) Express

\tan \theta

in simplest form. (b) Determine

\sin \theta

\cos \theta

\sec \theta

\csc \theta

and

\cot \theta

. (c) Verify that

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

using your answers from part (b).