4. Triangular & Circular Functions

4.01 Trigonometric functions as right triangle ratios

4.02 Special right triangles and exact value trigonometric ratios

4.03 Degrees, radians, and angles as rotations

4.04 Trigonometric functions in the coordinate plane

4.05 Trigonometric functions on the unit circle

4.06 Evaluating trigonometric functions: exact values

4.07 Extension: Relating the tangent to the slope of a line

United States of America

Grades 9-12

4.01 Trigonometric functions as right triangle ratios

Interactive practice questions

Evaluate $\sin\theta$sinθ within $\triangle ABC$△ABC.

A right triangle labeled with vertices $A$A, $B$B, and $C$C. The right angle is located at vertex $C$C as indicated by the small square. Each of the non-right angles is marked with a small arc near the vertex. The triangle has two angles labeled: angle α (alpha) at vertex $A$A and angle θ (theta) at vertex $B$B. Side $BC$BC, opposite to angle α (alpha), measures $6$ units. Side $AC$AC, opposite to angle θ (theta), measures $8$ units. Side $AB$AB, the hypotenuse that is opposite to the right angle, measures $10$ units.

Easy

< 1min

Evaluate $\cos\theta$cosθ within $\triangle ABC$△ABC. Express your answer as a simplified fraction.

Easy

< 1min

Evaluate $\sin\theta$sinθ within $\triangle ABC$△ABC. Express your answer as a simplified fraction.

Easy

< 1min

Consider the triangle in the figure. If $\sin\theta=\frac{4}{5}$sinθ=45:

Easy

3min

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