Question

C. Find the sum: sin60+cos30.

Answer 1

The sum of sin60 and cos30 is √3 since sin60 is equal to cos30 and the sum simplifies to 2 times cos30, which is √3.

Step-by-step explanation:

The question involves finding the sum of trigonometric functions sin60 and cos30. Since the sine of an angle is equal to the cosine of its complement, i.e., sin(90° - θ) = cos(θ), and both angles here are complementary (60° + 30° = 90°), we know that sin60° = cos30°. Therefore, the sum is simply sin60 + cos30 = cos30 + cos30 = 2cos30.

Using the unit circle or trigonometric values for common angles, we know that cos30° is equal to √3/2. Therefore, the sum simplifies to 2(√3/2), which equals √3. Thus, the answer to the student's question is √3.

Answer 2

sin60+cos30

Step-by-step explanation:

[tex] \frac{ \sqrt{3} }{2} + \frac{ \sqrt{3} }{2} \\ \\ \frac{2 \sqrt{3} + 2 \sqrt{3} }{4} \\ \frac{4 \sqrt{3} }{4 } \\ \sqrt{3} [tex]