1. Convert the following into remaining two units of measurements of an angle: (a) 60°, (b) 3.67°, (c) (11/6) R. 2. Evaluate: (a) cot 75°, (b) tan(25π/2), (c) tan(π/8). 3. Prove th... 1. Convert the following into remaining two units of measurements of an angle: (a) 60°, (b) 3.67°, (c) (11/6) R. 2. Evaluate: (a) cot 75°, (b) tan(25π/2), (c) tan(π/8). 3. Prove that: sin(A+B)sin(A-B) = sin²A sin²B. 4. Show that: tan 56° = (cos 11° + sin 11°) / (cos 11° - sin 11°). 5. Prove that: (1 + sin θ - cos θ) / (1 + sin θ + cos θ) = tan(θ/2). 6. Prove that: √(1 - cos 2θ) / 2 = sin θ. 7. In ΔABC, prove that tan A + tan B + tan C = tan A tan B tan C. 8. Prove that: √(2 + √(2 + 2cos θ)) = -2 cos θ. 9. Evaluate: sin 10° sin 30° sin 50° sin 70°. 10. Draw the graph of 3 sin(πx/2) (-2π < x < 2π). Read more

Steps to Solve

1. Convert 60° into radians and degrees To convert degrees to radians, use the conversion factor: $$ R = D \times \frac{\pi}{180} $$ For 60°: $$ R = 60 \times \frac{\pi}{180} = \frac{\pi}{3} \text{ rad} $$

2. Convert 3.57 into degrees and radians First, convert 3.57 radians into degrees using: $$ D = R \times \frac{180}{\pi} $$ For 3.57: $$ D = 3.57 \times \frac{180}{\pi} \approx 204.25° $$

3. Convert $\frac{\pi}{6}$ into degrees and radians To convert radians to degrees: $$ D = R \times \frac{180}{\pi} $$ For $\frac{\pi}{6}$: $$ D = \frac{\pi}{6} \times \frac{180}{\pi} = 30° $$

4. Evaluate cot 75° Using cotangent, we have: $$ \cot 75° = \frac{1}{\tan 75°} $$

5. Evaluate tan $\frac{25\pi}{2}$ Since $\frac{25\pi}{2}$ is greater than $2\pi$, reduce it by subtracting $12\pi$ (since $2\pi \approx 6.28$): $$ \frac{25\pi}{2} - 12\pi = \frac{\pi}{2} $$ Thus: $$ \tan\left(\frac{25\pi}{2}\right) = \tan\left(\frac{\pi}{2}\right) \text{ (undefined)} $$

6. Evaluate tan $\frac{\pi}{8}$ Using the definition of tangent: $$ \tan\left(\frac{\pi}{8}\right) = \frac{\sin\left(\frac{\pi}{8}\right)}{\cos\left(\frac{\pi}{8}\right)} $$