how do I find the sin, cos, and tan of -60 degrees without using a calculator?
Memorize the sides and angle of a 30-60 right triangle.
but what do i do for the negative part? just switch it to the opposite?
To find the values of sine, cosine, and tangent of -60 degrees without using a calculator, we can rely on the special angles in the unit circle and some basic trigonometric identities.
First, let's consider the angle -60 degrees. We know that the reference angle for -60 degrees is 60 degrees (since both angles have the same terminal arm).
Now, let's analyze the unit circle for the reference angle of 60 degrees:
- For sin(60 degrees), we look at the y-coordinate of the point on the unit circle corresponding to the reference angle. In this case, the y-coordinate is √3/2.
- For cos(60 degrees), we look at the x-coordinate of the point on the unit circle corresponding to the reference angle. In this case, the x-coordinate is 1/2.
- For tan(60 degrees), we calculate the ratio of sin(60 degrees) to cos(60 degrees). So, tan(60 degrees) is equal to (√3/2) / (1/2), which simplifies to √3.
Now, since the original angle -60 degrees is in the third quadrant, the signs of sin, cos, and tan will be negative.
Therefore, the values of sin(-60 degrees), cos(-60 degrees), and tan(-60 degrees) are -√3/2, -1/2, and -√3, respectively.