Answer:
The angles do not have the same reference angle.
Step-by-step explanation:
1) Angle 5π / 3 radians:
Convert radians to degrees: 5π/3 × 180° / π = 300°
300° is in the fourth quadrant
The reference angle for angles in the fourth quadrant is 360° - angle ⇒ 360° - 300° = 60°.
∴ The reference angle for this angle is 60°.
2) Angle 5π / 6 radians:
Convert radians to degrees: 5π/6 × 180° / π = 150°
150° is in the second quadrant
The reference angle for angles in the second quadrant is 180° - angle ⇒ 180° - 150° = 30°.
∴ The reference angle for this angle is 30°.
3) Conclusion:
Since the reference angles are different, the tangent ratios have different values.
tan (5π/3) = - tan(60°) = - √3
tan (5π/6) = - tan(30°) = - (√3)/3
Note that the tangent is negative in both second and fourth quadrants.
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Answer:
Step-by-step explanation:
<u>Properties of Logarithms</u>
We'll recall below the basic properties of logarithms:
Logarithm of the base:
Product rule:
Division rule:
Power rule:
Change of base:
Simplifying logarithms often requires the application of one or more of the above properties.
Simplify
Factoring 
.
Applying the power rule:
Since
Applying the power rule:
Applying the logarithm of the base:
Answer:
0.1375
Step-by-step explanation:
Answer:
Correct!
Step-by-step explanation:
You did it the correct mathematical way, where you divide 4 by 30. Some people get confused and multiply 30 and 4, so good job!
