# Find the Other Trig Values in Quadrant III csc(theta)=- square root of 2

Find the Other Trig Values in Quadrant III csc(theta)=- square root of 2
Use the definition of cosecant to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.
Find the adjacent side of the unit circle triangle. Since the hypotenuse and opposite sides are known, use the Pythagorean theorem to find the remaining side.
Replace the known values in the equation.
Negate .
Rewrite as .
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Multiply by by adding the exponents.
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Raise to the power of .
Subtract from .
Any root of is .
Multiply by .
Find the value of sine.
Use the definition of sine to find the value of .
Substitute in the known values.
Simplify the value of .
Move the negative in front of the fraction.
Multiply by .
Combine and simplify the denominator.
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Find the value of cosine.
Use the definition of cosine to find the value of .
Substitute in the known values.
Simplify the value of .
Move the negative in front of the fraction.
Multiply by .
Combine and simplify the denominator.
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Find the value of tangent.
Use the definition of tangent to find the value of .
Substitute in the known values.
Divide by .
Find the value of cotangent.
Use the definition of cotangent to find the value of .
Substitute in the known values.
Divide by .
Find the value of secant.
Use the definition of secant to find the value of .
Substitute in the known values.
Simplify the value of .
Move the negative one from the denominator of .
Rewrite as .
This is the solution to each trig value.
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### Name

Name one hundred seven million three hundred forty-one thousand one hundred fifty-eight

### Interesting facts

• 107341158 has 16 divisors, whose sum is 214859376
• The reverse of 107341158 is 851143701
• Previous prime number is 1333

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 30
• Digital Root 3

### Name

Name two billion fourteen million seven hundred thirty-two thousand four hundred fifty-eight

### Interesting facts

• 2014732458 has 8 divisors, whose sum is 3041851428
• The reverse of 2014732458 is 8542374102
• Previous prime number is 153

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 36
• Digital Root 9

### Name

Name one billion twenty million one hundred sixty thousand nine hundred thirty-five

### Interesting facts

• 1020160935 has 16 divisors, whose sum is 2176343424
• The reverse of 1020160935 is 5390610201
• Previous prime number is 5

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 27
• Digital Root 9