Back to Use special triangles and unit circle — Problem 2 · Task Set 68

Exercises: Exact Trigonometric Values from Special Triangles

Use special triangles and unit circle symmetry. Express all answers in exact form (no decimals).

Grade 9·22 problems·~30 min·Common Core Math - HS Functions·group·hsf-tf-a-3

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Fluency Practice

Find the exact value. Show the special triangle you used.

$30-60-90 triangle inscribed in the unit circle with the 30-degree angle at origin, vertical leg 1/2, horizontal leg sqrt(3)/2$

An equilateral triangle with side length 2 is bisected to form a 30-60-90 triangle with sides 1, $\sqrt{3}$ , and 2. When scaled to hypotenuse 1 and placed in the unit circle at angle $\frac{\pi}{6}$ , what is $\sin\!\left(\frac{\pi}{6}\right)$ ?