Property 4
Definition of the Trigonometric Functions (Right Triangle)
\(\cos\alpha=\samefrac{a}{c}\)
\(\sin\alpha=\samefrac{b}{c}\)
\(\tan\alpha=\samefrac{b}{a}\)
\(\cot\alpha=\samefrac{a}{b}\)
1.
\(sin\alpha=?\)
\(cos\alpha=?\)
\(tan\alpha=?\)
\(cot\alpha=?\)
2.
\(sin\alpha=?\)
\(cos\alpha=?\)
\(tan\alpha=?\)
\(cot\alpha=?\)
3.
\(sin\alpha=?\)
\(cos\alpha=?\)
\(tan\alpha=?\)
\(cot\alpha=?\)
4.
\(for angles α and β: trig values?\)
Property 5
If one trigonometric value of an acute angle is given, other trigonometric values can be found by drawing a right triangle.
Example
\(0<\alpha<90^\circ,\ \tan\alpha=3\)
\(\sin\alpha=\samefrac3{\sqrt{10}},\ \cos\alpha=\samefrac1{\sqrt{10}},\ \cot\alpha=\samefrac13\)
1.
\(0
\(\tan x=\samefrac12\)
\(sin x=?\)
2.
\(0
\(\sin x=\samefrac45\)
\(tan x=?\)
3.
\(0
\(\sin x=\samefrac5{13}\)
\(cot x=?\)
4.
\(0
\(\tan x=\samefrac13\)
\(cos x+sin x=?\)
5.
ABCD square; E lies on DC
\(tan\alpha=?\)
6.
Figure consists of congruent squares
\(sin\alpha=?\)
7.
\(\sin\alpha=\samefrac45\)
\(x=?\)
8.
ABCD square; AE=8, EC=2
\(tan\alpha=?\)
9.
\(3\tan B=2\tan C\)
\(|AB|=?\)