Trigonometry

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In a 45°-45°-90° triangle, the sides are in the ratio 1:1:√2. Both shorter sides are equal, and the hypotenuse is √2 times the length of each shorter side. Example: If each shorter side is 3 cm, the h…

Answer

In a 30°-60°-90° triangle, the sides are in the ratio 1:√3:2. The shortest side (opposite 30°) : medium side (opposite 60°) : longest side (hypotenuse) = 1:√3:2. Example: If shortest side is 4 cm, the…

Answer

sin θ = opposite side / hypotenuse. It represents the ratio of the side opposite to angle θ to the hypotenuse. Example: In a right triangle with angle 30°, if hypotenuse = 10 cm and opposite side = 5 …

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cos θ = adjacent side / hypotenuse. It represents the ratio of the side adjacent to angle θ to the hypotenuse. Example: In a right triangle with angle 60°, if hypotenuse = 8 cm and adjacent side = 4 c…

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tan θ = opposite side / adjacent side. It represents the ratio of the side opposite to angle θ to the side adjacent to angle θ. Example: In a right triangle with angle 45°, if opposite = 7 cm and adja…

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sin 30° = 1/2, cos 30° = √3/2, tan 30° = 1/√3. These come from the 30°-60°-90° triangle ratios. Memory tip: For 30°, sine is the smallest (1/2), cosine is medium (√3/2), and tangent is 1/√3.

Answer

sin 45° = 1/√2, cos 45° = 1/√2, tan 45° = 1. These come from the 45°-45°-90° triangle ratios. Memory tip: For 45°, sine and cosine are equal (1/√2), and tangent is 1.

Answer

sin 60° = √3/2, cos 60° = 1/2, tan 60° = √3. These come from the 30°-60°-90° triangle ratios. Memory tip: For 60°, sine is large (√3/2), cosine is small (1/2), and tangent is √3.