Find the exact values of the following.
cos 270 degrees = 90 degrees, value = 0.
Sin 180 degrees = 180-90 = 90 = 1, but its supposed to be zero, don't know how to get that:\
Confused with tan 240 degrees as well.
for the first two, like I told you in the last post, look at the graphs
for tan 240°
1. where is the angle ? in III , so the answer is -
2. how far to the x-axis? 60°
so tan240° = -tan60° = √3/1 , (from the 30-60- 90 triangle ratio)
always check with your calculator
To find the exact values of trigonometric functions, we can use the unit circle and the reference angles. Let's break down each of the given questions.
1. cos 270 degrees:
To find the value of cos 270 degrees, we need to look at the unit circle. Since the cosine function represents the x-coordinate of a point on the unit circle, we need to find the x-coordinate for the angle 270 degrees. If you visualize the unit circle, you will see that the point on the unit circle at 270 degrees is (-1, 0). Therefore, the value of cos 270 degrees is 0.
2. sin 180 degrees:
To find the value of sin 180 degrees, we again refer to the unit circle. The sine function represents the y-coordinate of a point on the unit circle. At 180 degrees, the point on the unit circle is (0, -1). So, the value of sin 180 degrees is -1, not 1. It seems like you made a mistake in your calculation. Please double-check your calculation for sin 180 degrees.
3. tan 240 degrees:
To find the value of tan 240 degrees, we can use the tangent function, which is defined as the ratio of sine to cosine. In this case, we need to find the ratio of sin 240 degrees to cos 240 degrees. Using the unit circle, we find that the point at 240 degrees is (-√3/2, -1/2). Therefore, sin 240 degrees = -1/2 and cos 240 degrees = -√3/2. Now, we can calculate tan 240 degrees by dividing these two values: tan 240 degrees = (sin 240 degrees) / (cos 240 degrees) = (-1/2) / (-√3/2). Simplifying this expression, we have tan 240 degrees = 1/√3 = √3/3.
Remember to use the unit circle and reference angles to find the values of trigonometric functions accurately.