For which angles beta, with 0 degrees less than/equal to beta less than/equal to 180 degrees,
is sin 3beta equal to -1?
a) 30 degress and 150 degrees
b) 60 and 120 degrees
c) 90 degrees
d) 0 and 120 degrees
I think it is C because sin of (3 x 90 = 270) 270 degrees is -1?
Did I do this right? Or did I do something that cannot be done?
Thank you.
your answer is correct. :)
To find the angles beta for which sin 3beta is equal to -1, we need to do the following steps:
Step 1: Solve the equation sin 3beta = -1.
Step 2: Determine the values of beta within the given range (0 degrees ≤ beta ≤ 180 degrees) that satisfy this equation.
Now let's go through these steps to find the correct answer:
Step 1: Solve the equation sin 3beta = -1.
To find the angles beta that satisfy sin 3beta = -1, we need to find the values of beta for which the sine function is equal to -1. Remember that the sine function is negative in the third and fourth quadrants of the unit circle.
Since we want to find angles beta within the given range (0 degrees ≤ beta ≤ 180 degrees), we only need to consider the fourth quadrant. In the fourth quadrant, the reference angle alpha for which sin alpha = 1 is 90 degrees.
So we have:
3beta = 180 - alpha
3beta = 180 - 90
3beta = 90
beta = 30
Step 2: Determine the values of beta within the given range (0 degrees ≤ beta ≤ 180 degrees) that satisfy this equation.
From the above calculation, we found that beta = 30 degrees satisfies the equation sin 3beta = -1.
Therefore, the correct answer is option A: 30 degrees and 150 degrees.
Regarding your choice of option C (90 degrees), you made a mistake in your calculation. It is not sin(3 x 90 = 270) degrees that should be -1, but rather sin(3 x 90) degrees which is equal to sin(270 degrees). However, sine of 270 degrees is not equal to -1, but rather -1. Therefore, option C is not correct.