For the angle shown is a point given on its terminal arm. [picture shows -12, -5 in quadrant three of the unit circle].
Calculate the values of the three primary trigonmetric ratios, accurate to four decimal places.
Dont understand thissss
sin = x/r = -12/13
cos = y/r = -5/13
tan = y/x = 5/12
...
rats. I mixed up sin and cos.
To calculate the values of the three primary trigonometric ratios (sine, cosine, and tangent) for the given angle, we can use the coordinates of the point on the terminal arm of the angle in the unit circle.
From the given picture, we can see that the point on the terminal arm of the angle is (-12, -5) in quadrant three of the unit circle.
To calculate the values of the three primary trigonometric ratios, we need to determine the lengths of the sides of the right triangle formed by the point on the terminal arm of the angle and the origin (0, 0).
Using the Pythagorean theorem, we can find the length of the hypotenuse (r) of the right triangle:
r = √((-12)^2 + (-5)^2)
r = √(144 + 25)
r = √169
r = 13
Now, we can calculate the values of the three primary trigonometric ratios:
1. Sine (sinθ):
sinθ = y / r
sinθ = -5 / 13 ≈ -0.3846
2. Cosine (cosθ):
cosθ = x / r
cosθ = -12 / 13 ≈ -0.9231
3. Tangent (tanθ):
tanθ = y / x
tanθ = -5 / -12 ≈ 0.4167
Therefore, the values of the three primary trigonometric ratios for the given angle (accurate to four decimal places) are as follows:
- Sine (sinθ) ≈ -0.3846
- Cosine (cosθ) ≈ -0.9231
- Tangent (tanθ) ≈ 0.4167