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Values of Significant Angles

Values of Significant Angles

The trigonometric values of certain angles should be known:

Angle Sin Cos Tan
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

Example 2

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