Property 7
Trigonometric Values of 30°, 40°, 60°
\(\tan45^\circ=1\)
\(\cot45^\circ=1\)
\(\sin45^\circ=\samefrac1{\sqrt2}=\samefrac{\sqrt2}2\)
\(\cos45^\circ=\samefrac1{\sqrt2}=\samefrac{\sqrt2}2\)
\(\longrightarrow\)
\(\sin30^\circ=\samefrac12\)
\(\cos30^\circ=\samefrac{\sqrt3}2\)
\(\tan30^\circ=\samefrac1{\sqrt3}=\samefrac{\sqrt3}3\)
\(\cot30^\circ=\sqrt3\)
\(\sin60^\circ=\samefrac{\sqrt3}2\)
\(\cos60^\circ=\samefrac12\)
\(\tan60^\circ=\sqrt3\)
\(\cot60^\circ=\samefrac{\sqrt3}3\)
1.
\(\sin30^\circ+\tan60^\circ=?\)
2.
\(\cos45^\circ-\cot45^\circ=?\)
3.
\(\samefrac{\sin30^\circ-\cos30^\circ}{\cot30^\circ}=?\)
4.
\(\samefrac{\cos45^\circ-\sin45^\circ}{\cot60^\circ}=?\)
5.
\(\samefrac{\sin60^\circ+\cos30^\circ}{\tan60^\circ}=?\)
6.
\(\samefrac{\tan30^\circ\cdot\cos30^\circ}{\sin60^\circ}=?\)
7.
\(\samefrac{\tan\left(\samefrac{\pi}{4}\right)+\cot\left(\samefrac{\pi}{4}\right)}{\sin\left(\samefrac{\pi}{6}\right)}=?\)
8.
\(\samefrac{\sin\left(\samefrac\pi3\right)}{\tan\left(\samefrac\pi6\right)}=?\)
9.
\(\samefrac{\cot\left(\samefrac{\pi}{3}\right)\cos\left(\samefrac{\pi}{6}\right)}{\tan\left(\samefrac{\pi}{4}\right)}=?\)
Property 8
\(\alpha+\beta=90^\circ\)
\(\sin\alpha=\cos\beta\)
\(\tan\alpha=\cot\beta\)
1.
\(\samefrac{\sin20^\circ}{\cos70^\circ}=?\)
2.
\(\samefrac{\tan15^\circ+\cot50^\circ}{\cot75^\circ+\tan40^\circ}=?\)
3.
\(\samefrac{3\sin40^\circ+\cos50^\circ}{\cos50^\circ}=?\)
4.
\(\sin^220^\circ+\sin^270^\circ+2\tan10^\circ\cdot\tan80^\circ=?\)
5.
\(\samefrac{\sin22^\circ}{\cos68^\circ}-2+3\cdot\tan5^\circ\cdot\tan85^\circ=?\)
6.
\(\cos^210^\circ+\cos^280^\circ-\samefrac{2\sin10^\circ}{\cos80^\circ}=?\)
7.
\(\samefrac{\cos24^\circ+\sin34^\circ}{\sin66^\circ+\cos56^\circ}=?\)
8.
\(2\sin^2\samefrac{5\pi}{16}+2\sin^2\samefrac{3\pi}{16}=?\)
9.
\(\cos20^\circ\cdot\operatorname{cosec}20^\circ\cdot\cot70^\circ=?\)
10.
\(\samefrac{\tan\left(\samefrac\pi7\right)\cdot\tan\left(\samefrac{5\pi}{14}\right)}{\sin^2\left(\samefrac\pi{10}\right)+\sin^2\left(\samefrac{2\pi}5\right)}=?\)
11.
\(\samefrac{\sin18^\circ-\sin45^\circ+\sin72^\circ}{\cos18^\circ-\cos45^\circ+\cos72^\circ}=?\)
12.
\(\samefrac{\cot25^\circ}{\tan65^\circ}+1+\sin^240^\circ+\samefrac1{\sec^240^\circ}=?\)