Property 7
Trigonometric Values of 30°, 45°, 60°
| angle | sin | cos | tan | cot |
|---|---|---|---|---|
| 30° | 1/2 | √3/2 | 1/√3 | √3 |
| 45° | √2/2 | √2/2 | 1 | 1 |
| 60° | √3/2 | 1/2 | √3 | 1/√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.
\(\samefrac{\tan30^\circ\cos30^\circ}{\sin60^\circ}=?\)
7.
\(\samefrac{\tan(\pi/4)+\cot(\pi/4)}{\sin(\pi/6)}=?\)
8.
\(\samefrac{\sin(3\pi/3)}{\tan(\pi/6)}=?\)
9.
\(\samefrac{\cot(\pi/3)\cos(\pi/6)}{\tan(\pi/4)}=?\)
Property 8
If \(\alpha+\beta=90^\circ\), then \(\sin\alpha=\cos\beta\) and \(\tan\alpha=\cot\beta\).
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.
\(\sin^220^\circ+\sin^270^\circ+2\tan10^\circ\tan80^\circ=?\)
5.
\(\samefrac{\sin22^\circ}{\cos68^\circ}-2+3\tan5^\circ\tan85^\circ=?\)
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.
\(\cos20^\circ\csc20^\circ\cot70^\circ=?\)
10.
\(\samefrac{\tan(\pi/7)\tan(5\pi/14)}{\sin^2(\pi/10)+\sin^2(2\pi/5)}=?\)
11.
\(\samefrac{\sin18^\circ-\sin45^\circ+\sin72^\circ}{\cos18^\circ-\cos45^\circ+\cos72^\circ}=?\)
12.
\(\samefrac{\cot25^\circ}{\tan65^\circ}+1+\sin^240^\circ-\samefrac1{\sec^240^\circ}=?\)