I had to find the sine, cosine and tangent of -150 degrees. I got - sq. root of 3/2, -1/2, and - sq. root of 3/3. But my book has -1/2 as the sine, and -sq. root of 3/3 as the cosine. Why is this? I thought that it was thirty degrees away from the axis, so I should use pi/3.
No. -150deg is not PI/3
To find the sine, cosine, and tangent of angles, it's important to understand the unit of measurement being used. In this case, both degrees and radians are being mentioned.
Firstly, let's clarify the unit of measurement being used. Degrees measure angles in a circle, where one full revolution is 360 degrees. On the other hand, radians measure angles in terms of the radius of a circle. One full revolution is equal to 2π radians, where π (pi) is approximately 3.14159.
Now, let's address the specific angle of -150 degrees. When we convert -150 degrees to radians, we can use the formula:
Radian measure = (Degree measure × π) / 180
By substituting the given value, we have:
Radian measure = (-150 × π) / 180 = -5π / 6
Hence, -150 degrees is equivalent to -5π / 6 radians.
Now, let's proceed to find the sine, cosine, and tangent of -150 degrees (-5π / 6 radians).
To determine these trigonometric ratios, it's helpful to refer to the unit circle. The unit circle is a circle with a radius of 1 unit, centered at the origin (0, 0) on a coordinate plane.
For -5π / 6 radians (or -150 degrees), we find the corresponding point on the unit circle. At this angle, the x-coordinate will give us the cosine, and the y-coordinate will give us the sine.
Since -5π / 6 corresponds to the third quadrant in the unit circle, both the sine and cosine values will be negative.
The correct values for the sine, cosine, and tangent of -150 degrees (-5π / 6 radians) are as follows:
Sine: -1/2
Cosine: -√3 / 2 (approximately -0.866)
Tangent: √3 / 3 (approximately 0.577)
Therefore, your book is correct in stating that the sine is -1/2 and the cosine is -√3 / 2. The values you obtained (-√3 / 2 and -√3 / 3) are not accurate for -150 degrees (-5π / 6 radians).