Exercises
Put your trigonometry skills to the test with this Trigonometric Angle Relationships Quiz. Answer questions about the values of sine, cosine, tangent, cotangent, secant, and cosecant at common angles such as 0°, 30°, 45°, 60°, 90°, and 180°. You will also explore a basic geometric angle relationship involving perpendicular lines. Ideal for students reviewing unit-circle values, special-angle trigonometry, and foundational angle concepts.
Answer the questions below and check the explanation for each answer.
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The sine of a 90-degree angle is 1, as this corresponds to the maximum value on the unit circle where the angle is at the topmost point.
The cosine of a 180-degree angle is -1, because on the unit circle, moving 180 degrees from the origin ends at the leftmost point.
The tangent of a 45-degree angle is 1, as both the sine and cosine of 45 degrees are equal, making their ratio equal to 1.
The sine of 30 degrees is 0.5 and cosine of 60 degrees is also 0.5. Adding them gives a total of 1.
The cotangent is the reciprocal of tangent. At 0 degrees, the tangent is 0, making cotangent undefined as division by zero is not allowed.
The secant is the reciprocal of cosine. For a 60-degree angle, the cosine is 0.5, so the secant is 2/√3.
The cosecant is the reciprocal of sine. The sine of a 90-degree angle is 1, so its reciprocal, or cosecant, is also 1.
The sine of a 0-degree angle is 0 as it represents the horizontal position on the unit circle where the vertical component is zero.
The cosine of a 90-degree angle is 0 because the point is at the vertical topmost part of the unit circle with no horizontal component.
The angle between a line and its perpendicular is 90 degrees, as they form a right angle by definition.
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