Question
Given that sin 0 = -0.865, where 3 pi / 2 < 0 < 2pi. Find the value of cos 0 and then tan 0.
Round your values to 3 decimal places.
Round your values to 3 decimal places.
Answers
GPT 3.5
To find the value of cos 0, we can use the trigonometric identity sin^2 0 + cos^2 0 = 1.
Given sin 0 = -0.865, we can substitute in the value of sin 0 and solve for cos 0:
(-0.865)^2 + cos^2 0 = 1
0.748 + cos^2 0 = 1
cos^2 0 = 0.252
cos 0 ≈ √0.252
cos 0 ≈ 0.502
Now we can find the value of tan 0 by using the trigonometric identity tan 0 = sin 0 / cos 0:
tan 0 = -0.865 / 0.502
tan 0 ≈ -1.723
Therefore, the value of cos 0 is approximately 0.502 and the value of tan 0 is approximately -1.723.
Given sin 0 = -0.865, we can substitute in the value of sin 0 and solve for cos 0:
(-0.865)^2 + cos^2 0 = 1
0.748 + cos^2 0 = 1
cos^2 0 = 0.252
cos 0 ≈ √0.252
cos 0 ≈ 0.502
Now we can find the value of tan 0 by using the trigonometric identity tan 0 = sin 0 / cos 0:
tan 0 = -0.865 / 0.502
tan 0 ≈ -1.723
Therefore, the value of cos 0 is approximately 0.502 and the value of tan 0 is approximately -1.723.