Trigonometrical Ratios of Standard Angles

Answer

Step 1: Use the standard-angle values. Step 2: sin 30° = 1/2. Step 3: cos 60° = 1/2. Step 4: tan 60° = √3. Answer: sin 30° = 1/2, cos 60° = 1/2, tan 60° = √3.

Answer

Step 1: Recall the standard values at 0°. Step 2: sin 0° = 0. Step 3: cos 0° = 1. Answer: sin 0° = 0 and cos 0° = 1.

Answer

Step 1: Recall the standard values at 90°. Step 2: sin 90° = 1. Step 3: cos 90° = 0. Answer: sin 90° = 1 and cos 90° = 0.

Answer

Step 1: Use tan θ = sin θ / cos θ. Step 2: At 90°, sin 90° = 1 and cos 90° = 0. Step 3: Division by 0 is not defined. Answer: tan 90° is not defined.

Answer

Step 1: Use cot θ = cos θ / sin θ. Step 2: At 0°, cos 0° = 1 and sin 0° = 0. Step 3: Division by 0 is not defined. Answer: cot 0° is not defined.

Answer

Step 1: In an equilateral triangle, BC = 2a. Step 2: D is the foot of the perpendicular from A to BC, so BD = BC/2. Step 3: BD = 2a/2 = a. Answer: BD = a.

Answer

Step 1: Use Pythagoras in right triangle ABD. Step 2: AD² = AB² - BD². Step 3: AD² = (2a)² - a² = 4a² - a² = 3a². Step 4: AD = √3·a. Answer: AD = √3·a.

Answer

Step 1: Each angle of an equilateral triangle is 60°. Step 2: So ∠B = 60°. Step 3: AD is perpendicular to BC, so ∠ADB = 90°. Step 4: The remaining angle is 180° - (60° + 90°) = 30°. Answer: ∠B = 60° a…