Values of Significant Angles

Values of Significant Angles

GCSE(F), GCSE(H),

The trigonometric values of certain angles should be known:

AngleSinCosTan
010
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)`
90º10undefined

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

Examples

1. What is the value of the angle ABC?

Answer: 45º

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

2. What is the value of the angle BAC?

Answer: 60º

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