Question 13 of 50beginner🔧 ApplyVery Short1 mark

Find the values of the trigonometric functions: sin 765°

Correct Answer

sin 765° = 12\frac{1}{\sqrt{2}}

Exercise: EXERCISE 3.2 | Q: 6 | (Page 15)
For More Understanding

Explanation

This question tests the concept of periodicity of trigonometric functions. The textbook demonstrates in Example 9 that trigonometric values repeat after intervals of 360°. Students need to reduce the given angle to an equivalent angle within the first rotation (0° to 360°) and then use the standard values from the table provided in the context.

Solution Steps

  1. Step 1: We know that values of sin x repeat after an interval of 2π or 360°.

  2. Step 2: Reduce 765° to an equivalent angle: 765° = 765° - 2×3602 \times 360° = 765° - 720° = 45°

  3. Step 3: Therefore, sin 765° = sin 45°

  4. Step 4: From the standard values table, sin 45° = 12\frac{1}{\sqrt{2}}

  5. Step 5: Hence, sin 765° = 12\frac{1}{\sqrt{2}}

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