Values of Significant Angles

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The trigonometric values of certain angles should be known:

Angle	Sin	Cos	Tan
0º	0	1	0
30º	$frac(1)(2)$	$frac(√3)(2)$	$frac(1)(√3)$
45º	$frac(1)(√2)$	$frac(1)(√2)$	1
60º	$frac(√3)(2)$	$frac(1)(2)$	$sqrt(3)$
90º	1	0	undefined

The entry for tan 90º is undefined as the value is infinity.

Example 1

What is the value of the angle ABC?

Knowing common values of angles with shorted sides of 2

The adjacent and opposite values are known.

The tan of an angle is given by $frac(text(opp))(text(adj))$ = $frac(2)(2)$ = 1.

The angle with a tan value of 1 is 45º

Answer: 45º

What is the value of the angle BAC?

Knowing common values of angles with side of root 2 and hypotenuse of 2

The hypotenuse and opposite sides are known.

The sine of the angle is given by $frac(text(opp))(text(hype))$ = $frac(sqrt(3))(2)$ = 60º

Answer: 60º