Answer the following with respect to the angle .

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Answer the following with respect to the angle

75^{\circ}

. (a) Write

75^{\circ}

as a sum or difference of two standard angles whose exact sine and cosine values are known. (b) Find the exact value of

\sin 75^{\circ}

. (c) Find the exact value of

\cos 75^{\circ}

. (d) Using the above results, calculate

\tan 75^{\circ}

in its simplest surd form.