State the related acute angle for sin(-π/3) and then find the exact value
I am getting 60 degrees, is this correct?
actually, -60º ... what's the sine?
I'm not sure you mean when you say "what is the sine"
the question asks for the angle and "the exact value" of the sine
That's what I'm asking about, I'm not sure what the "exact value" is. In fact, I'm not really sure if I've got the right "related acute angle"
sin - 60 = - (1/2) sqrt 3
1, sqrt 3 , 2 right triangle
To find the related acute angle for sin(-π/3) and determine its exact value, you need to use the symmetry property of trigonometric functions.
1. Start by finding the reference angle. The reference angle is the positive acute angle formed between the terminal side of the angle and the x-axis in the standard position.
In this case, the angle is -π/3, which lies in the third quadrant. To find the reference angle, determine the positive acute angle formed between the terminal side and the x-axis, which is the same as finding the angle's absolute value. The absolute value of -π/3 is π/3.
2. The related acute angle is found by taking the reference angle and determining its complementary angle. Since the sine function is positive in both the first and second quadrants, the related acute angle will be the complementary angle to the reference angle.
The complementary angle of π/3 is the angle that, when added to π/3, equals π/2. Therefore, the related acute angle is π/2 - π/3 = π/6.
3. Finally, you can find the exact value of sin(π/6) using the known values of sine in the first quadrant. In the first quadrant, the sine of π/6 is 1/2.
So, the related acute angle for sin(-π/3) is π/6, and its exact value is 1/2.
Therefore, the answer to your question is no, the related acute angle for sin(-π/3) is π/6, not 60 degrees.