In geometry and trigonometry, the phrase “specific angle” usually refers either to the exact angle being solved for in a given problem or to “special angles” ( 0∘0 raised to the composed with power 30∘30 raised to the composed with power 45∘45 raised to the composed with power 60∘60 raised to the composed with power 90∘90 raised to the composed with power
) that yield exact, predictable values on the unit circle without using a calculator. Individual Angle Classifications
Every unique angle size falls under a specific mathematical category based entirely on its degree or radian measurement: Acute Angle: Any angle that measures strictly between 0∘0 raised to the composed with power 90∘90 raised to the composed with power Right Angle: An angle that measures exactly 90∘90 raised to the composed with power
π2the fraction with numerator pi and denominator 2 end-fraction radians). It forms a perfect perpendicular corner. Obtuse Angle: An angle greater than 90∘90 raised to the composed with power but less than 180∘180 raised to the composed with power Straight Angle: An angle measuring exactly 180∘180 raised to the composed with power radians), which forms a flat straight line. Reflex Angle: An angle that is greater than 180∘180 raised to the composed with power but less than 360∘360 raised to the composed with power Full Rotation / Perigon: An angle of exactly 360∘360 raised to the composed with power radians), representing one complete circle. The Five Special Trigonometric Angles
In trigonometry, a specific subset of angles is widely memorized because they correspond to the exact side lengths of standard geometric shapes, like bisected squares ( 45∘45 raised to the composed with power 45∘45 raised to the composed with power 90∘90 raised to the composed with power ) and equilateral triangles ( 30∘30 raised to the composed with power 60∘60 raised to the composed with power 90∘90 raised to the composed with power
The precise values for these special angles are outlined below: Angle in Degrees Angle in Radians Sine Value ( Cosine Value ( Tangent Value ( tantangent 0∘0 raised to the composed with power 30∘30 raised to the composed with power
π6the fraction with numerator pi and denominator 6 end-fraction 12one-half
32the fraction with numerator the square root of 3 end-root and denominator 2 end-fraction
33the fraction with numerator the square root of 3 end-root and denominator 3 end-fraction 45∘45 raised to the composed with power
π4the fraction with numerator pi and denominator 4 end-fraction
22the fraction with numerator the square root of 2 end-root and denominator 2 end-fraction
22the fraction with numerator the square root of 2 end-root and denominator 2 end-fraction 60∘60 raised to the composed with power
π3the fraction with numerator pi and denominator 3 end-fraction
32the fraction with numerator the square root of 3 end-root and denominator 2 end-fraction 12one-half 3the square root of 3 end-root 90∘90 raised to the composed with power
π2the fraction with numerator pi and denominator 2 end-fraction Undefined Geometric Specific Angle Relationships
Angles are also given specific structural names based on how they pair up or relate to neighboring lines: How do you find the angle? Let’s see…
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