Exercises
Challenge your understanding of core trigonometric functions and their applications in right triangles. This quiz covers sine, cosine, and tangent ratios, along with essential values for special angles such as 0°, 30°, 45°, 60°, and 90°. Practice identifying opposite and adjacent side relationships, recognizing which functions are defined at key angles, and recalling fundamental trig values. Ideal for students building confidence with introductory trigonometry concepts.
Answer the questions below and check the explanation for each answer.
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The sine of 90° is 1 because it represents the maximum vertical position on the unit circle.
The tangent of 45° is 1 as it equals the ratio in a 45°-45°-90° triangle, where opposite equals adjacent.
The cosine of 0° is 1 because it represents the maximum horizontal position on the unit circle.
The tangent function is the ratio of the opposite side to the adjacent side in a right triangle.
The cosine of 60° is 0.5, indicating half of the radius of the unit circle along the horizontal axis.
tan(30°) is √3/3, obtained as the ratio of the sides in a 30°-60°-90° triangle.
The tangent of 90° is undefined because the tangent function involves division by zero (adjacent side).
The sine of 30° is 0.5, derived from the ratio in a 30°-60°-90° triangle.
For θ = 45°, tangent is equal to 1 because opposite and adjacent sides are equal in a 45° triangle.
The cosine of 90° is 0 as it represents no horizontal movement on the unit circle.
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