If 5cosA+3=0 and 180(degrees)<A<360(degrees)
Determine
1. Tan^2A
And
2. SinA over cosA
This is the third time you've posted this question. See the related questions below. What seems to be the trouble?
1.39/16
The answer is 0.086875.
To determine the values of Tan^2A and SinA/CosA, we first need to find the value of A that satisfies the given equation 5cosA + 3 = 0 and the restrictions 180° < A < 360°.
Let's solve the equation 5cosA + 3 = 0:
1. Subtract 3 from both sides:
5cosA = -3
2. Divide both sides by 5:
cosA = -3/5
Now, we can find the value of A by taking the inverse cosine (cos⁻¹) of -3/5.
3. Use a calculator to find the inverse cosine of -3/5:
A ≈ cos⁻¹(-3/5) ≈ 143.13°
Note that the inverse cosine function only returns values between 0° and 180°, so we need to determine if A lies in the desired range of 180° < A < 360°.
4. Since A ≈ 143.13° is less than 180°, we need to find the angle in the second quadrant that has the same cosine value. This is done by subtracting the angle from 180°:
180° - 143.13° ≈ 36.87°
Therefore, we have two possible solutions for A: A ≈ 143.13° and A ≈ 36.87°.
Now, let's calculate Tan^2A and SinA/CosA for each solution:
1. Tan^2A:
For the first solution, A ≈ 143.13°:
- Calculate the tangent of 143.13°:
tan(143.13°) ≈ 1.106
- Square the tangent value:
1.106^2 ≈ 1.225
For the second solution, A ≈ 36.87°:
- Calculate the tangent of 36.87°:
tan(36.87°) ≈ 0.753
- Square the tangent value:
0.753^2 ≈ 0.566
Therefore, the values of Tan^2A for the given equation are approximately 1.225 and 0.566.
2. SinA/CosA:
For the first solution, A ≈ 143.13°:
- Calculate the sine of 143.13°:
sin(143.13°) ≈ -0.787
- Calculate the cosine of 143.13°:
cos(143.13°) ≈ -0.617
- Divide the sine by the cosine:
(-0.787) / (-0.617) ≈ 1.275
For the second solution, A ≈ 36.87°:
- Calculate the sine of 36.87°:
sin(36.87°) ≈ 0.598
- Calculate the cosine of 36.87°:
cos(36.87°) ≈ 0.802
- Divide the sine by the cosine:
(0.598) / (0.802) ≈ 0.745
Therefore, the values of SinA/CosA for the given equation are approximately 1.275 and 0.745.