# Find Trig Functions Using Identities tan(theta)=24/7 , sin(theta)<0

Find Trig Functions Using Identities tan(theta)=24/7 , sin(theta)<0
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The sine function is negative in the third and fourth quadrants. The tangent function is positive in the first and third quadrants. The set of solutions for are limited to the third quadrant since that is the only quadrant found in both sets.
Solution is in the third quadrant.
Use the definition of tangent to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.
Find the hypotenuse of the unit circle triangle. Since the opposite and adjacent sides are known, use the Pythagorean theorem to find the remaining side.
Replace the known values in the equation.
Raise to the power of .
Hypotenuse
Raise to the power of .
Hypotenuse
Hypotenuse
Rewrite as .
Hypotenuse
Pull terms out from under the radical, assuming positive real numbers.
Hypotenuse
Hypotenuse
Find the value of sine.
Use the definition of sine to find the value of .
Substitute in the known values.
Move the negative in front of the fraction.
Find the value of cosine.
Use the definition of cosine to find the value of .
Substitute in the known values.
Move the negative in front of the fraction.
Find the value of cotangent.
Use the definition of cotangent to find the value of .
Substitute in the known values.
Dividing two negative values results in a positive value.
Find the value of secant.
Use the definition of secant to find the value of .
Substitute in the known values.
Move the negative in front of the fraction.
Find the value of cosecant.
Use the definition of cosecant to find the value of .
Substitute in the known values.
Move the negative in front of the fraction.
This is the solution to each trig value.
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### Name

Name four hundred sixteen million four hundred forty thousand five hundred seventy-one

### Interesting facts

• 416440571 has 4 divisors, whose sum is 416929632
• The reverse of 416440571 is 175044614
• Previous prime number is 853

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 32
• Digital Root 5

### Name

Name one billion three hundred eighty-seven million four hundred twenty thousand forty-two

### Interesting facts

• 1387420042 has 16 divisors, whose sum is 2113511040
• The reverse of 1387420042 is 2400247831
• Previous prime number is 563

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 31
• Digital Root 4

### Name

Name one billion four hundred fifty-five million nine hundred thirty thousand three hundred ninety-one

### Interesting facts

• 1455930391 has 4 divisors, whose sum is 1461466512
• The reverse of 1455930391 is 1930395541
• Previous prime number is 263

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 40
• Digital Root 4