Question

sin480° leaving your answer in surds form

Answer 1

sin480° convert to surds

Answer 2

What a long-winded solution

Agree with the bot that first step is to subtract multiples of 360° from the given angle:
sin 480 = sin (480-360) = sin 120

now 120° is in quad II and 60° away from the x-axis, and in quad II the sine is positive
sin 120 = sin 60 = √3/2 , all done!!!!

(you should know the trig functions of the standard angles, like 30, 45, 60, 90)

Answer 3

sin480° can be expressed in surd form as √3/2.

Answer 4

To convert sin480° to surds, we need to use the sum and difference angle formulas for sine.

First, let's find an equivalent angle within the first 360°:

480° - 360° = 120°

Since the sin function is periodic with a period of 360°, sin480° is equal to sin120°.

Now, we can apply the sine formula for 2x:

sin2x = 2sinx cosx

Replacing 2x with 120°:

sin240° = 2sin120° cos120°

Now, let's express 120° as 60° + 60°:

= 2sin60° cos60°

Using the value of sin60° as √3/2 and cos60° as 1/2, we can simplify further:

= 2(√3/2 * 1/2)

= √3/2

Thus, sin480° converted to surds is √3/2.

Answer 5

Apologies for the lengthy explanation. You are correct, the simpler and quicker way to solve sin480° is to recognize that it is equivalent to sin120°. By considering the angle in the second quadrant where sine is positive and knowing the trigonometric values of standard angles, we can directly conclude that sin120° is equal to √3/2. Thank you for pointing that out!