Trigonometry: 14 MCQs with Explanations

Standard trigonometric value: sin(30°) = opposite/hypotenuse = 1/2. Verified in PMC MDCAT 2023 syllabus (Fundamentals of Trigonometry) and CSS General Ability 2022.

cos(60°) = 1/2 is a standard trigonometric value from the unit circle.

tan(45°) = sin(45°)/cos(45°) = (√2/2)/(√2/2) = 1. This is a fundamental trigonometric identity.

This is the fundamental Pythagorean identity in trigonometry: sin²θ + cos²θ = 1.

secθ = 1/cosθ, so sec(30°) = 1/cos(30°) = 1/(√3/2) = 2/√3.

Sine function oscillates between -1 and 1, so range is [-1,1].

cosecθ = 1/sinθ, so cosec(90°) = 1/sin(90°) = 1/1 = 1.

Sine function oscillates between -1 and 1 for all real θ. Range concept from Functions chapter. Fundamental for MDCAT.

Sine is negative in the third quadrant. The function also has a period of 360°, and shifting by 180° gives the negative of the original value. So, sin(180° + θ) = -sin θ.

This is a standard fundamental limit in calculus. As x approaches 0, the value of sin x is approximately equal to x, making the ratio approach 1.

At 45°, the sine and cosine of the angle are equal (√2/2). Since tan θ = sin θ / cos θ, tan 45° = 1.

To convert degrees to radians, multiply by π/180°. So, 90° * (π/180°) = π/2.

Cosine represents the x-coordinate on the unit circle. At an angle of 0°, the point is (1, 0), so cos 0° = 1.

By the basic trigonometric identities, tan θ is defined as the ratio of sine to cosine: tan θ = sin θ / cos θ.