TANGENT THE UNIT CIRCLE. REMEMBER Find x in the right triangle above. x 1 30° Find y in the right triangle below. y Using your calculator, what is the.

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Presentation transcript:

TANGENT THE UNIT CIRCLE

REMEMBER Find x in the right triangle above. x 1 30° Find y in the right triangle below. y Using your calculator, what is the cos 30°? Using your calculator, what is the sin 30°? Aim: Know exact values of critical angles in order to simplify expressions. ≈

TANGENT According to SohCahToa = cosθ 1 θ Aim: Know exact values of critical angles in order to simplify expressions. Cah Toa x y = sinθ Soh

QUADRANT I 30° 1 0°30°45°60°90° sinθ cosθ tan θ 0°30°45°60°90° sinθ cosθ tan θ Exact Values Approximate Values 1 45° 1 60° 1 90° 1 Aim: Know exact values of critical angles in order to simplify expressions.

ON THE UNIT CIRCLE sinθ θ tanθ θ θ θ Aim: Know exact values of critical angles in order to simplify expressions.

WHERE ARE THE POSITIVES? All Students Take Calculus SinSin TanTan CosCos AllAll Aim: Know exact values of critical angles in order to simplify expressions.

TRY THESE 1. If cosθ > 0 and tanθ < 0, which quadrant is the terminating ray of an angle in standard position. 2. The point is on the terminal side of an angle θ in standard position. If the distance of the point from the origin is one unit, find sinθ and tanθ. 3.Find the exact value of sin (-135°). 4.Simplify: (cos 30°)(sin 60°) – tan 60° Aim: Know exact values of critical angles in order to simplify expressions.